[{"data":1,"prerenderedAt":9657},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgram-schmidt-verfahren":546,"formula-related-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgram-schmidt-verfahren":9644},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":312,"checks":9561,"conditions":9599,"conditionsHtml":9600,"deprecated":9601,"description":9555,"extension":9602,"figure":9601,"figureCaption":9601,"figureHtml":9601,"formulaId":9603,"latex":9604,"latexHtml":9605,"level":9606,"meta":9607,"navigation":9608,"path":9609,"redirectFrom":9610,"related":9611,"seo":9616,"stem":9617,"subject":581,"summary":9618,"tags":9619,"variables":9624,"__hash__":9643},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgram-schmidt-verfahren.md","Gram-Schmidt-Verfahren",[550,551,552,553,554],"Gram-Schmidtsches Orthogonalisierungsverfahren","Orthonormalbasis berechnen","Vektoren orthogonalisieren","ONB bestimmen","Orthogonalisierung",{"type":556,"value":557,"toc":9554},"minimark",[558,563,1289,1292,2359,3092,3511,3515,4043,4447,5367,6680,7167,8064,8068],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,570,571,849,850,853,854,1068,1069,853,1072,1288],"p",{},"Das ",[568,569,548],"strong",{}," macht aus linear unabhängigen Vektoren ",[572,573,576,633],"span",{"className":574},[575],"katex",[572,577,580],{"className":578},[579],"katex-mathml",[581,582,584],"math",{"xmlns":583},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[585,586,587,628],"semantics",{},[588,589,590,609,612,615,617],"mrow",{},[591,592,593,605],"msub",{},[594,595,597,601],"mover",{"accent":596},"true",[598,599,600],"mi",{},"v",[602,603,604],"mo",{},"⃗",[606,607,608],"mn",{},"1",[602,610,611],{"separator":596},",",[602,613,614],{},"…",[602,616,611],{"separator":596},[591,618,619,625],{},[594,620,621,623],{"accent":596},[598,622,600],{},[602,624,604],{},[598,626,627],{},"n",[629,630,632],"annotation",{"encoding":631},"application\u002Fx-tex","\\vec v_1, \\ldots, \\vec v_n",[572,634,637],{"className":635,"ariaHidden":596},[636],"katex-html",[572,638,641,646,754,758,763,767,770,773,776],{"className":639},[640],"base",[572,642],{"className":643,"style":645},[644],"strut","height:0.9084em;vertical-align:-0.1944em;",[572,647,650,708],{"className":648},[649],"mord",[572,651,654],{"className":652},[649,653],"accent",[572,655,658],{"className":656},[657],"vlist-t",[572,659,662],{"className":660},[661],"vlist-r",[572,663,667,680],{"className":664,"style":666},[665],"vlist","height:0.714em;",[572,668,670,675],{"style":669},"top:-3em;",[572,671],{"className":672,"style":674},[673],"pstrut","height:3em;",[572,676,600],{"className":677,"style":679},[649,678],"mathnormal","margin-right:0.0359em;",[572,681,682,685],{"style":669},[572,683],{"className":684,"style":674},[673],[572,686,690],{"className":687,"style":689},[688],"accent-body","left:-0.2077em;",[572,691,695],{"className":692,"style":694},[693],"overlay","height:0.714em;width:0.471em;",[696,697,704],"svg",{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[705,706],"path",{"d":707},"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z",[572,709,712],{"className":710},[711],"msupsub",[572,713,716,745],{"className":714},[657,715],"vlist-t2",[572,717,719,740],{"className":718},[661],[572,720,723],{"className":721,"style":722},[665],"height:0.3011em;",[572,724,726,730],{"style":725},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[572,727],{"className":728,"style":729},[673],"height:2.7em;",[572,731,737],{"className":732},[733,734,735,736],"sizing","reset-size6","size3","mtight",[572,738,608],{"className":739},[649,736],[572,741,744],{"className":742},[743],"vlist-s","​",[572,746,748],{"className":747},[661],[572,749,752],{"className":750,"style":751},[665],"height:0.15em;",[572,753],{},[572,755,611],{"className":756},[757],"mpunct",[572,759],{"className":760,"style":762},[761],"mspace","margin-right:0.1667em;",[572,764,614],{"className":765},[766],"minner",[572,768],{"className":769,"style":762},[761],[572,771,611],{"className":772},[757],[572,774],{"className":775,"style":762},[761],[572,777,779,814],{"className":778},[649],[572,780,782],{"className":781},[649,653],[572,783,785],{"className":784},[657],[572,786,788],{"className":787},[661],[572,789,791,799],{"className":790,"style":666},[665],[572,792,793,796],{"style":669},[572,794],{"className":795,"style":674},[673],[572,797,600],{"className":798,"style":679},[649,678],[572,800,801,804],{"style":669},[572,802],{"className":803,"style":674},[673],[572,805,807],{"className":806,"style":689},[688],[572,808,810],{"className":809,"style":694},[693],[696,811,812],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,813],{"d":707},[572,815,817],{"className":816},[711],[572,818,820,841],{"className":819},[657,715],[572,821,823,838],{"className":822},[661],[572,824,827],{"className":825,"style":826},[665],"height:0.1514em;",[572,828,829,832],{"style":725},[572,830],{"className":831,"style":729},[673],[572,833,835],{"className":834},[733,734,735,736],[572,836,627],{"className":837},[649,678,736],[572,839,744],{"className":840},[743],[572,842,844],{"className":843},[661],[572,845,847],{"className":846,"style":751},[665],[572,848],{}," ein ",[568,851,852],{},"Orthogonalsystem"," ",[572,855,857,896],{"className":856},[575],[572,858,860],{"className":859},[579],[581,861,862],{"xmlns":583},[585,863,864,893],{},[588,865,866,877,879,881,883],{},[591,867,868,875],{},[594,869,870,873],{"accent":596},[598,871,872],{},"u",[602,874,604],{},[606,876,608],{},[602,878,611],{"separator":596},[602,880,614],{},[602,882,611],{"separator":596},[591,884,885,891],{},[594,886,887,889],{"accent":596},[598,888,872],{},[602,890,604],{},[598,892,627],{},[629,894,895],{"encoding":631},"\\vec u_1, \\ldots, \\vec u_n",[572,897,899],{"className":898,"ariaHidden":596},[636],[572,900,902,905,978,981,984,987,990,993,996],{"className":901},[640],[572,903],{"className":904,"style":645},[644],[572,906,908,943],{"className":907},[649],[572,909,911],{"className":910},[649,653],[572,912,914],{"className":913},[657],[572,915,917],{"className":916},[661],[572,918,920,928],{"className":919,"style":666},[665],[572,921,922,925],{"style":669},[572,923],{"className":924,"style":674},[673],[572,926,872],{"className":927},[649,678],[572,929,930,933],{"style":669},[572,931],{"className":932,"style":674},[673],[572,934,936],{"className":935,"style":689},[688],[572,937,939],{"className":938,"style":694},[693],[696,940,941],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,942],{"d":707},[572,944,946],{"className":945},[711],[572,947,949,970],{"className":948},[657,715],[572,950,952,967],{"className":951},[661],[572,953,955],{"className":954,"style":722},[665],[572,956,958,961],{"style":957},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[572,959],{"className":960,"style":729},[673],[572,962,964],{"className":963},[733,734,735,736],[572,965,608],{"className":966},[649,736],[572,968,744],{"className":969},[743],[572,971,973],{"className":972},[661],[572,974,976],{"className":975,"style":751},[665],[572,977],{},[572,979,611],{"className":980},[757],[572,982],{"className":983,"style":762},[761],[572,985,614],{"className":986},[766],[572,988],{"className":989,"style":762},[761],[572,991,611],{"className":992},[757],[572,994],{"className":995,"style":762},[761],[572,997,999,1034],{"className":998},[649],[572,1000,1002],{"className":1001},[649,653],[572,1003,1005],{"className":1004},[657],[572,1006,1008],{"className":1007},[661],[572,1009,1011,1019],{"className":1010,"style":666},[665],[572,1012,1013,1016],{"style":669},[572,1014],{"className":1015,"style":674},[673],[572,1017,872],{"className":1018},[649,678],[572,1020,1021,1024],{"style":669},[572,1022],{"className":1023,"style":674},[673],[572,1025,1027],{"className":1026,"style":689},[688],[572,1028,1030],{"className":1029,"style":694},[693],[696,1031,1032],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1033],{"d":707},[572,1035,1037],{"className":1036},[711],[572,1038,1040,1060],{"className":1039},[657,715],[572,1041,1043,1057],{"className":1042},[661],[572,1044,1046],{"className":1045,"style":826},[665],[572,1047,1048,1051],{"style":957},[572,1049],{"className":1050,"style":729},[673],[572,1052,1054],{"className":1053},[733,734,735,736],[572,1055,627],{"className":1056},[649,678,736],[572,1058,744],{"className":1059},[743],[572,1061,1063],{"className":1062},[661],[572,1064,1066],{"className":1065,"style":751},[665],[572,1067],{},", das denselben Raum aufspannt. Normiert man anschließend, erhält man eine ",[568,1070,1071],{},"Orthonormalbasis",[572,1073,1075,1114],{"className":1074},[575],[572,1076,1078],{"className":1077},[579],[581,1079,1080],{"xmlns":583},[585,1081,1082,1111],{},[588,1083,1084,1095,1097,1099,1101],{},[591,1085,1086,1093],{},[594,1087,1088,1091],{"accent":596},[598,1089,1090],{},"w",[602,1092,604],{},[606,1094,608],{},[602,1096,611],{"separator":596},[602,1098,614],{},[602,1100,611],{"separator":596},[591,1102,1103,1109],{},[594,1104,1105,1107],{"accent":596},[598,1106,1090],{},[602,1108,604],{},[598,1110,627],{},[629,1112,1113],{"encoding":631},"\\vec w_1, \\ldots, \\vec w_n",[572,1115,1117],{"className":1116,"ariaHidden":596},[636],[572,1118,1120,1123,1198,1201,1204,1207,1210,1213,1216],{"className":1119},[640],[572,1121],{"className":1122,"style":645},[644],[572,1124,1126,1163],{"className":1125},[649],[572,1127,1129],{"className":1128},[649,653],[572,1130,1132],{"className":1131},[657],[572,1133,1135],{"className":1134},[661],[572,1136,1138,1147],{"className":1137,"style":666},[665],[572,1139,1140,1143],{"style":669},[572,1141],{"className":1142,"style":674},[673],[572,1144,1090],{"className":1145,"style":1146},[649,678],"margin-right:0.0269em;",[572,1148,1149,1152],{"style":669},[572,1150],{"className":1151,"style":674},[673],[572,1153,1156],{"className":1154,"style":1155},[688],"left:-0.1522em;",[572,1157,1159],{"className":1158,"style":694},[693],[696,1160,1161],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1162],{"d":707},[572,1164,1166],{"className":1165},[711],[572,1167,1169,1190],{"className":1168},[657,715],[572,1170,1172,1187],{"className":1171},[661],[572,1173,1175],{"className":1174,"style":722},[665],[572,1176,1178,1181],{"style":1177},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[572,1179],{"className":1180,"style":729},[673],[572,1182,1184],{"className":1183},[733,734,735,736],[572,1185,608],{"className":1186},[649,736],[572,1188,744],{"className":1189},[743],[572,1191,1193],{"className":1192},[661],[572,1194,1196],{"className":1195,"style":751},[665],[572,1197],{},[572,1199,611],{"className":1200},[757],[572,1202],{"className":1203,"style":762},[761],[572,1205,614],{"className":1206},[766],[572,1208],{"className":1209,"style":762},[761],[572,1211,611],{"className":1212},[757],[572,1214],{"className":1215,"style":762},[761],[572,1217,1219,1254],{"className":1218},[649],[572,1220,1222],{"className":1221},[649,653],[572,1223,1225],{"className":1224},[657],[572,1226,1228],{"className":1227},[661],[572,1229,1231,1239],{"className":1230,"style":666},[665],[572,1232,1233,1236],{"style":669},[572,1234],{"className":1235,"style":674},[673],[572,1237,1090],{"className":1238,"style":1146},[649,678],[572,1240,1241,1244],{"style":669},[572,1242],{"className":1243,"style":674},[673],[572,1245,1247],{"className":1246,"style":1155},[688],[572,1248,1250],{"className":1249,"style":694},[693],[696,1251,1252],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1253],{"d":707},[572,1255,1257],{"className":1256},[711],[572,1258,1260,1280],{"className":1259},[657,715],[572,1261,1263,1277],{"className":1262},[661],[572,1264,1266],{"className":1265,"style":826},[665],[572,1267,1268,1271],{"style":1177},[572,1269],{"className":1270,"style":729},[673],[572,1272,1274],{"className":1273},[733,734,735,736],[572,1275,627],{"className":1276},[649,678,736],[572,1278,744],{"className":1279},[743],[572,1281,1283],{"className":1282},[661],[572,1284,1286],{"className":1285,"style":751},[665],[572,1287],{},".",[564,1290,1291],{},"Schritte:",[1293,1294,1295,1507,2047],"ol",{},[1296,1297,1298,1288],"li",{},[572,1299,1301,1336],{"className":1300},[575],[572,1302,1304],{"className":1303},[579],[581,1305,1306],{"xmlns":583},[585,1307,1308,1333],{},[588,1309,1310,1320,1323],{},[591,1311,1312,1318],{},[594,1313,1314,1316],{"accent":596},[598,1315,872],{},[602,1317,604],{},[606,1319,608],{},[602,1321,1322],{},"=",[591,1324,1325,1331],{},[594,1326,1327,1329],{"accent":596},[598,1328,600],{},[602,1330,604],{},[606,1332,608],{},[629,1334,1335],{"encoding":631},"\\vec u_1 = \\vec v_1",[572,1337,1339,1429],{"className":1338,"ariaHidden":596},[636],[572,1340,1342,1346,1418,1422,1426],{"className":1341},[640],[572,1343],{"className":1344,"style":1345},[644],"height:0.864em;vertical-align:-0.15em;",[572,1347,1349,1384],{"className":1348},[649],[572,1350,1352],{"className":1351},[649,653],[572,1353,1355],{"className":1354},[657],[572,1356,1358],{"className":1357},[661],[572,1359,1361,1369],{"className":1360,"style":666},[665],[572,1362,1363,1366],{"style":669},[572,1364],{"className":1365,"style":674},[673],[572,1367,872],{"className":1368},[649,678],[572,1370,1371,1374],{"style":669},[572,1372],{"className":1373,"style":674},[673],[572,1375,1377],{"className":1376,"style":689},[688],[572,1378,1380],{"className":1379,"style":694},[693],[696,1381,1382],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1383],{"d":707},[572,1385,1387],{"className":1386},[711],[572,1388,1390,1410],{"className":1389},[657,715],[572,1391,1393,1407],{"className":1392},[661],[572,1394,1396],{"className":1395,"style":722},[665],[572,1397,1398,1401],{"style":957},[572,1399],{"className":1400,"style":729},[673],[572,1402,1404],{"className":1403},[733,734,735,736],[572,1405,608],{"className":1406},[649,736],[572,1408,744],{"className":1409},[743],[572,1411,1413],{"className":1412},[661],[572,1414,1416],{"className":1415,"style":751},[665],[572,1417],{},[572,1419],{"className":1420,"style":1421},[761],"margin-right:0.2778em;",[572,1423,1322],{"className":1424},[1425],"mrel",[572,1427],{"className":1428,"style":1421},[761],[572,1430,1432,1435],{"className":1431},[640],[572,1433],{"className":1434,"style":1345},[644],[572,1436,1438,1473],{"className":1437},[649],[572,1439,1441],{"className":1440},[649,653],[572,1442,1444],{"className":1443},[657],[572,1445,1447],{"className":1446},[661],[572,1448,1450,1458],{"className":1449,"style":666},[665],[572,1451,1452,1455],{"style":669},[572,1453],{"className":1454,"style":674},[673],[572,1456,600],{"className":1457,"style":679},[649,678],[572,1459,1460,1463],{"style":669},[572,1461],{"className":1462,"style":674},[673],[572,1464,1466],{"className":1465,"style":689},[688],[572,1467,1469],{"className":1468,"style":694},[693],[696,1470,1471],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1472],{"d":707},[572,1474,1476],{"className":1475},[711],[572,1477,1479,1499],{"className":1478},[657,715],[572,1480,1482,1496],{"className":1481},[661],[572,1483,1485],{"className":1484,"style":722},[665],[572,1486,1487,1490],{"style":725},[572,1488],{"className":1489,"style":729},[673],[572,1491,1493],{"className":1492},[733,734,735,736],[572,1494,608],{"className":1495},[649,736],[572,1497,744],{"className":1498},[743],[572,1500,1502],{"className":1501},[661],[572,1503,1505],{"className":1504,"style":751},[665],[572,1506],{},[1296,1508,1509,1510,1595,1596,1703,1704,1815,1816,1288],{},"Für ",[572,1511,1513,1541],{"className":1512},[575],[572,1514,1516],{"className":1515},[579],[581,1517,1518],{"xmlns":583},[585,1519,1520,1538],{},[588,1521,1522,1525,1527,1530,1532,1534,1536],{},[598,1523,1524],{},"k",[602,1526,1322],{},[606,1528,1529],{},"2",[602,1531,611],{"separator":596},[602,1533,614],{},[602,1535,611],{"separator":596},[598,1537,627],{},[629,1539,1540],{"encoding":631},"k = 2, \\ldots, n",[572,1542,1544,1564],{"className":1543,"ariaHidden":596},[636],[572,1545,1547,1551,1555,1558,1561],{"className":1546},[640],[572,1548],{"className":1549,"style":1550},[644],"height:0.6944em;",[572,1552,1524],{"className":1553,"style":1554},[649,678],"margin-right:0.0315em;",[572,1556],{"className":1557,"style":1421},[761],[572,1559,1322],{"className":1560},[1425],[572,1562],{"className":1563,"style":1421},[761],[572,1565,1567,1571,1574,1577,1580,1583,1586,1589,1592],{"className":1566},[640],[572,1568],{"className":1569,"style":1570},[644],"height:0.8389em;vertical-align:-0.1944em;",[572,1572,1529],{"className":1573},[649],[572,1575,611],{"className":1576},[757],[572,1578],{"className":1579,"style":762},[761],[572,1581,614],{"className":1582},[766],[572,1584],{"className":1585,"style":762},[761],[572,1587,611],{"className":1588},[757],[572,1590],{"className":1591,"style":762},[761],[572,1593,627],{"className":1594},[649,678],": Von ",[572,1597,1599,1621],{"className":1598},[575],[572,1600,1602],{"className":1601},[579],[581,1603,1604],{"xmlns":583},[585,1605,1606,1618],{},[588,1607,1608],{},[591,1609,1610,1616],{},[594,1611,1612,1614],{"accent":596},[598,1613,600],{},[602,1615,604],{},[598,1617,1524],{},[629,1619,1620],{"encoding":631},"\\vec v_k",[572,1622,1624],{"className":1623,"ariaHidden":596},[636],[572,1625,1627,1630],{"className":1626},[640],[572,1628],{"className":1629,"style":1345},[644],[572,1631,1633,1668],{"className":1632},[649],[572,1634,1636],{"className":1635},[649,653],[572,1637,1639],{"className":1638},[657],[572,1640,1642],{"className":1641},[661],[572,1643,1645,1653],{"className":1644,"style":666},[665],[572,1646,1647,1650],{"style":669},[572,1648],{"className":1649,"style":674},[673],[572,1651,600],{"className":1652,"style":679},[649,678],[572,1654,1655,1658],{"style":669},[572,1656],{"className":1657,"style":674},[673],[572,1659,1661],{"className":1660,"style":689},[688],[572,1662,1664],{"className":1663,"style":694},[693],[696,1665,1666],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1667],{"d":707},[572,1669,1671],{"className":1670},[711],[572,1672,1674,1695],{"className":1673},[657,715],[572,1675,1677,1692],{"className":1676},[661],[572,1678,1681],{"className":1679,"style":1680},[665],"height:0.3361em;",[572,1682,1683,1686],{"style":725},[572,1684],{"className":1685,"style":729},[673],[572,1687,1689],{"className":1688},[733,734,735,736],[572,1690,1524],{"className":1691,"style":1554},[649,678,736],[572,1693,744],{"className":1694},[743],[572,1696,1698],{"className":1697},[661],[572,1699,1701],{"className":1700,"style":751},[665],[572,1702],{}," werden die orthogonalen Projektionen auf alle bisherigen ",[572,1705,1707,1730],{"className":1706},[575],[572,1708,1710],{"className":1709},[579],[581,1711,1712],{"xmlns":583},[585,1713,1714,1727],{},[588,1715,1716],{},[591,1717,1718,1724],{},[594,1719,1720,1722],{"accent":596},[598,1721,872],{},[602,1723,604],{},[598,1725,1726],{},"j",[629,1728,1729],{"encoding":631},"\\vec u_j",[572,1731,1733],{"className":1732,"ariaHidden":596},[636],[572,1734,1736,1740],{"className":1735},[640],[572,1737],{"className":1738,"style":1739},[644],"height:1.0001em;vertical-align:-0.2861em;",[572,1741,1743,1778],{"className":1742},[649],[572,1744,1746],{"className":1745},[649,653],[572,1747,1749],{"className":1748},[657],[572,1750,1752],{"className":1751},[661],[572,1753,1755,1763],{"className":1754,"style":666},[665],[572,1756,1757,1760],{"style":669},[572,1758],{"className":1759,"style":674},[673],[572,1761,872],{"className":1762},[649,678],[572,1764,1765,1768],{"style":669},[572,1766],{"className":1767,"style":674},[673],[572,1769,1771],{"className":1770,"style":689},[688],[572,1772,1774],{"className":1773,"style":694},[693],[696,1775,1776],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1777],{"d":707},[572,1779,1781],{"className":1780},[711],[572,1782,1784,1806],{"className":1783},[657,715],[572,1785,1787,1803],{"className":1786},[661],[572,1788,1791],{"className":1789,"style":1790},[665],"height:0.3117em;",[572,1792,1793,1796],{"style":957},[572,1794],{"className":1795,"style":729},[673],[572,1797,1799],{"className":1798},[733,734,735,736],[572,1800,1726],{"className":1801,"style":1802},[649,678,736],"margin-right:0.0572em;",[572,1804,744],{"className":1805},[743],[572,1807,1809],{"className":1808},[661],[572,1810,1813],{"className":1811,"style":1812},[665],"height:0.2861em;",[572,1814],{}," abgezogen. Was übrig bleibt, steht senkrecht auf allen ",[572,1817,1819,1864],{"className":1818},[575],[572,1820,1822],{"className":1821},[579],[581,1823,1824],{"xmlns":583},[585,1825,1826,1861],{},[588,1827,1828,1838,1840,1842,1844],{},[591,1829,1830,1836],{},[594,1831,1832,1834],{"accent":596},[598,1833,872],{},[602,1835,604],{},[606,1837,608],{},[602,1839,611],{"separator":596},[602,1841,614],{},[602,1843,611],{"separator":596},[591,1845,1846,1852],{},[594,1847,1848,1850],{"accent":596},[598,1849,872],{},[602,1851,604],{},[588,1853,1854,1856,1859],{},[598,1855,1524],{},[602,1857,1858],{},"−",[606,1860,608],{},[629,1862,1863],{"encoding":631},"\\vec u_1, \\ldots, \\vec u_{k-1}",[572,1865,1867],{"className":1866,"ariaHidden":596},[636],[572,1868,1870,1874,1946,1949,1952,1955,1958,1961,1964],{"className":1869},[640],[572,1871],{"className":1872,"style":1873},[644],"height:0.9223em;vertical-align:-0.2083em;",[572,1875,1877,1912],{"className":1876},[649],[572,1878,1880],{"className":1879},[649,653],[572,1881,1883],{"className":1882},[657],[572,1884,1886],{"className":1885},[661],[572,1887,1889,1897],{"className":1888,"style":666},[665],[572,1890,1891,1894],{"style":669},[572,1892],{"className":1893,"style":674},[673],[572,1895,872],{"className":1896},[649,678],[572,1898,1899,1902],{"style":669},[572,1900],{"className":1901,"style":674},[673],[572,1903,1905],{"className":1904,"style":689},[688],[572,1906,1908],{"className":1907,"style":694},[693],[696,1909,1910],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,1911],{"d":707},[572,1913,1915],{"className":1914},[711],[572,1916,1918,1938],{"className":1917},[657,715],[572,1919,1921,1935],{"className":1920},[661],[572,1922,1924],{"className":1923,"style":722},[665],[572,1925,1926,1929],{"style":957},[572,1927],{"className":1928,"style":729},[673],[572,1930,1932],{"className":1931},[733,734,735,736],[572,1933,608],{"className":1934},[649,736],[572,1936,744],{"className":1937},[743],[572,1939,1941],{"className":1940},[661],[572,1942,1944],{"className":1943,"style":751},[665],[572,1945],{},[572,1947,611],{"className":1948},[757],[572,1950],{"className":1951,"style":762},[761],[572,1953,614],{"className":1954},[766],[572,1956],{"className":1957,"style":762},[761],[572,1959,611],{"className":1960},[757],[572,1962],{"className":1963,"style":762},[761],[572,1965,1967,2002],{"className":1966},[649],[572,1968,1970],{"className":1969},[649,653],[572,1971,1973],{"className":1972},[657],[572,1974,1976],{"className":1975},[661],[572,1977,1979,1987],{"className":1978,"style":666},[665],[572,1980,1981,1984],{"style":669},[572,1982],{"className":1983,"style":674},[673],[572,1985,872],{"className":1986},[649,678],[572,1988,1989,1992],{"style":669},[572,1990],{"className":1991,"style":674},[673],[572,1993,1995],{"className":1994,"style":689},[688],[572,1996,1998],{"className":1997,"style":694},[693],[696,1999,2000],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2001],{"d":707},[572,2003,2005],{"className":2004},[711],[572,2006,2008,2038],{"className":2007},[657,715],[572,2009,2011,2035],{"className":2010},[661],[572,2012,2014],{"className":2013,"style":1680},[665],[572,2015,2016,2019],{"style":957},[572,2017],{"className":2018,"style":729},[673],[572,2020,2022],{"className":2021},[733,734,735,736],[572,2023,2025,2028,2032],{"className":2024},[649,736],[572,2026,1524],{"className":2027,"style":1554},[649,678,736],[572,2029,1858],{"className":2030},[2031,736],"mbin",[572,2033,608],{"className":2034},[649,736],[572,2036,744],{"className":2037},[743],[572,2039,2041],{"className":2040},[661],[572,2042,2045],{"className":2043,"style":2044},[665],"height:0.2083em;",[572,2046],{},[1296,2048,2049,2050,1288],{},"Jeden Vektor durch seine Länge teilen: ",[572,2051,2053,2107],{"className":2052},[575],[572,2054,2056],{"className":2055},[579],[581,2057,2058],{"xmlns":583},[585,2059,2060,2104],{},[588,2061,2062,2072,2074,2084,2088,2092,2102],{},[591,2063,2064,2070],{},[594,2065,2066,2068],{"accent":596},[598,2067,1090],{},[602,2069,604],{},[598,2071,1524],{},[602,2073,1322],{},[591,2075,2076,2082],{},[594,2077,2078,2080],{"accent":596},[598,2079,872],{},[602,2081,604],{},[598,2083,1524],{},[598,2085,2087],{"mathvariant":2086},"normal","\u002F",[602,2089,2091],{"stretchy":2090},"false","∥",[591,2093,2094,2100],{},[594,2095,2096,2098],{"accent":596},[598,2097,872],{},[602,2099,604],{},[598,2101,1524],{},[602,2103,2091],{"stretchy":2090},[629,2105,2106],{"encoding":631},"\\vec w_k = \\vec u_k \u002F \\lVert \\vec u_k \\rVert",[572,2108,2110,2197],{"className":2109,"ariaHidden":596},[636],[572,2111,2113,2116,2188,2191,2194],{"className":2112},[640],[572,2114],{"className":2115,"style":1345},[644],[572,2117,2119,2154],{"className":2118},[649],[572,2120,2122],{"className":2121},[649,653],[572,2123,2125],{"className":2124},[657],[572,2126,2128],{"className":2127},[661],[572,2129,2131,2139],{"className":2130,"style":666},[665],[572,2132,2133,2136],{"style":669},[572,2134],{"className":2135,"style":674},[673],[572,2137,1090],{"className":2138,"style":1146},[649,678],[572,2140,2141,2144],{"style":669},[572,2142],{"className":2143,"style":674},[673],[572,2145,2147],{"className":2146,"style":1155},[688],[572,2148,2150],{"className":2149,"style":694},[693],[696,2151,2152],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2153],{"d":707},[572,2155,2157],{"className":2156},[711],[572,2158,2160,2180],{"className":2159},[657,715],[572,2161,2163,2177],{"className":2162},[661],[572,2164,2166],{"className":2165,"style":1680},[665],[572,2167,2168,2171],{"style":1177},[572,2169],{"className":2170,"style":729},[673],[572,2172,2174],{"className":2173},[733,734,735,736],[572,2175,1524],{"className":2176,"style":1554},[649,678,736],[572,2178,744],{"className":2179},[743],[572,2181,2183],{"className":2182},[661],[572,2184,2186],{"className":2185,"style":751},[665],[572,2187],{},[572,2189],{"className":2190,"style":1421},[761],[572,2192,1322],{"className":2193},[1425],[572,2195],{"className":2196,"style":1421},[761],[572,2198,2200,2204,2276,2279,2283,2355],{"className":2199},[640],[572,2201],{"className":2202,"style":2203},[644],"height:1em;vertical-align:-0.25em;",[572,2205,2207,2242],{"className":2206},[649],[572,2208,2210],{"className":2209},[649,653],[572,2211,2213],{"className":2212},[657],[572,2214,2216],{"className":2215},[661],[572,2217,2219,2227],{"className":2218,"style":666},[665],[572,2220,2221,2224],{"style":669},[572,2222],{"className":2223,"style":674},[673],[572,2225,872],{"className":2226},[649,678],[572,2228,2229,2232],{"style":669},[572,2230],{"className":2231,"style":674},[673],[572,2233,2235],{"className":2234,"style":689},[688],[572,2236,2238],{"className":2237,"style":694},[693],[696,2239,2240],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2241],{"d":707},[572,2243,2245],{"className":2244},[711],[572,2246,2248,2268],{"className":2247},[657,715],[572,2249,2251,2265],{"className":2250},[661],[572,2252,2254],{"className":2253,"style":1680},[665],[572,2255,2256,2259],{"style":957},[572,2257],{"className":2258,"style":729},[673],[572,2260,2262],{"className":2261},[733,734,735,736],[572,2263,1524],{"className":2264,"style":1554},[649,678,736],[572,2266,744],{"className":2267},[743],[572,2269,2271],{"className":2270},[661],[572,2272,2274],{"className":2273,"style":751},[665],[572,2275],{},[572,2277,2087],{"className":2278},[649],[572,2280,2091],{"className":2281},[2282],"mopen",[572,2284,2286,2321],{"className":2285},[649],[572,2287,2289],{"className":2288},[649,653],[572,2290,2292],{"className":2291},[657],[572,2293,2295],{"className":2294},[661],[572,2296,2298,2306],{"className":2297,"style":666},[665],[572,2299,2300,2303],{"style":669},[572,2301],{"className":2302,"style":674},[673],[572,2304,872],{"className":2305},[649,678],[572,2307,2308,2311],{"style":669},[572,2309],{"className":2310,"style":674},[673],[572,2312,2314],{"className":2313,"style":689},[688],[572,2315,2317],{"className":2316,"style":694},[693],[696,2318,2319],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2320],{"d":707},[572,2322,2324],{"className":2323},[711],[572,2325,2327,2347],{"className":2326},[657,715],[572,2328,2330,2344],{"className":2329},[661],[572,2331,2333],{"className":2332,"style":1680},[665],[572,2334,2335,2338],{"style":957},[572,2336],{"className":2337,"style":729},[673],[572,2339,2341],{"className":2340},[733,734,735,736],[572,2342,1524],{"className":2343,"style":1554},[649,678,736],[572,2345,744],{"className":2346},[743],[572,2348,2350],{"className":2349},[661],[572,2351,2353],{"className":2352,"style":751},[665],[572,2354],{},[572,2356,2091],{"className":2357},[2358],"mclose",[564,2360,2361,2362,2390,2391,2603,2604,2816,2817,2922,2923,3091],{},"Für jedes ",[572,2363,2365,2378],{"className":2364},[575],[572,2366,2368],{"className":2367},[579],[581,2369,2370],{"xmlns":583},[585,2371,2372,2376],{},[588,2373,2374],{},[598,2375,1524],{},[629,2377,1524],{"encoding":631},[572,2379,2381],{"className":2380,"ariaHidden":596},[636],[572,2382,2384,2387],{"className":2383},[640],[572,2385],{"className":2386,"style":1550},[644],[572,2388,1524],{"className":2389,"style":1554},[649,678]," spannen ",[572,2392,2394,2432],{"className":2393},[575],[572,2395,2397],{"className":2396},[579],[581,2398,2399],{"xmlns":583},[585,2400,2401,2429],{},[588,2402,2403,2413,2415,2417,2419],{},[591,2404,2405,2411],{},[594,2406,2407,2409],{"accent":596},[598,2408,872],{},[602,2410,604],{},[606,2412,608],{},[602,2414,611],{"separator":596},[602,2416,614],{},[602,2418,611],{"separator":596},[591,2420,2421,2427],{},[594,2422,2423,2425],{"accent":596},[598,2424,872],{},[602,2426,604],{},[598,2428,1524],{},[629,2430,2431],{"encoding":631},"\\vec u_1, \\ldots, \\vec u_k",[572,2433,2435],{"className":2434,"ariaHidden":596},[636],[572,2436,2438,2441,2513,2516,2519,2522,2525,2528,2531],{"className":2437},[640],[572,2439],{"className":2440,"style":645},[644],[572,2442,2444,2479],{"className":2443},[649],[572,2445,2447],{"className":2446},[649,653],[572,2448,2450],{"className":2449},[657],[572,2451,2453],{"className":2452},[661],[572,2454,2456,2464],{"className":2455,"style":666},[665],[572,2457,2458,2461],{"style":669},[572,2459],{"className":2460,"style":674},[673],[572,2462,872],{"className":2463},[649,678],[572,2465,2466,2469],{"style":669},[572,2467],{"className":2468,"style":674},[673],[572,2470,2472],{"className":2471,"style":689},[688],[572,2473,2475],{"className":2474,"style":694},[693],[696,2476,2477],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2478],{"d":707},[572,2480,2482],{"className":2481},[711],[572,2483,2485,2505],{"className":2484},[657,715],[572,2486,2488,2502],{"className":2487},[661],[572,2489,2491],{"className":2490,"style":722},[665],[572,2492,2493,2496],{"style":957},[572,2494],{"className":2495,"style":729},[673],[572,2497,2499],{"className":2498},[733,734,735,736],[572,2500,608],{"className":2501},[649,736],[572,2503,744],{"className":2504},[743],[572,2506,2508],{"className":2507},[661],[572,2509,2511],{"className":2510,"style":751},[665],[572,2512],{},[572,2514,611],{"className":2515},[757],[572,2517],{"className":2518,"style":762},[761],[572,2520,614],{"className":2521},[766],[572,2523],{"className":2524,"style":762},[761],[572,2526,611],{"className":2527},[757],[572,2529],{"className":2530,"style":762},[761],[572,2532,2534,2569],{"className":2533},[649],[572,2535,2537],{"className":2536},[649,653],[572,2538,2540],{"className":2539},[657],[572,2541,2543],{"className":2542},[661],[572,2544,2546,2554],{"className":2545,"style":666},[665],[572,2547,2548,2551],{"style":669},[572,2549],{"className":2550,"style":674},[673],[572,2552,872],{"className":2553},[649,678],[572,2555,2556,2559],{"style":669},[572,2557],{"className":2558,"style":674},[673],[572,2560,2562],{"className":2561,"style":689},[688],[572,2563,2565],{"className":2564,"style":694},[693],[696,2566,2567],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2568],{"d":707},[572,2570,2572],{"className":2571},[711],[572,2573,2575,2595],{"className":2574},[657,715],[572,2576,2578,2592],{"className":2577},[661],[572,2579,2581],{"className":2580,"style":1680},[665],[572,2582,2583,2586],{"style":957},[572,2584],{"className":2585,"style":729},[673],[572,2587,2589],{"className":2588},[733,734,735,736],[572,2590,1524],{"className":2591,"style":1554},[649,678,736],[572,2593,744],{"className":2594},[743],[572,2596,2598],{"className":2597},[661],[572,2599,2601],{"className":2600,"style":751},[665],[572,2602],{}," denselben Raum auf wie ",[572,2605,2607,2645],{"className":2606},[575],[572,2608,2610],{"className":2609},[579],[581,2611,2612],{"xmlns":583},[585,2613,2614,2642],{},[588,2615,2616,2626,2628,2630,2632],{},[591,2617,2618,2624],{},[594,2619,2620,2622],{"accent":596},[598,2621,600],{},[602,2623,604],{},[606,2625,608],{},[602,2627,611],{"separator":596},[602,2629,614],{},[602,2631,611],{"separator":596},[591,2633,2634,2640],{},[594,2635,2636,2638],{"accent":596},[598,2637,600],{},[602,2639,604],{},[598,2641,1524],{},[629,2643,2644],{"encoding":631},"\\vec v_1, \\ldots, \\vec v_k",[572,2646,2648],{"className":2647,"ariaHidden":596},[636],[572,2649,2651,2654,2726,2729,2732,2735,2738,2741,2744],{"className":2650},[640],[572,2652],{"className":2653,"style":645},[644],[572,2655,2657,2692],{"className":2656},[649],[572,2658,2660],{"className":2659},[649,653],[572,2661,2663],{"className":2662},[657],[572,2664,2666],{"className":2665},[661],[572,2667,2669,2677],{"className":2668,"style":666},[665],[572,2670,2671,2674],{"style":669},[572,2672],{"className":2673,"style":674},[673],[572,2675,600],{"className":2676,"style":679},[649,678],[572,2678,2679,2682],{"style":669},[572,2680],{"className":2681,"style":674},[673],[572,2683,2685],{"className":2684,"style":689},[688],[572,2686,2688],{"className":2687,"style":694},[693],[696,2689,2690],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2691],{"d":707},[572,2693,2695],{"className":2694},[711],[572,2696,2698,2718],{"className":2697},[657,715],[572,2699,2701,2715],{"className":2700},[661],[572,2702,2704],{"className":2703,"style":722},[665],[572,2705,2706,2709],{"style":725},[572,2707],{"className":2708,"style":729},[673],[572,2710,2712],{"className":2711},[733,734,735,736],[572,2713,608],{"className":2714},[649,736],[572,2716,744],{"className":2717},[743],[572,2719,2721],{"className":2720},[661],[572,2722,2724],{"className":2723,"style":751},[665],[572,2725],{},[572,2727,611],{"className":2728},[757],[572,2730],{"className":2731,"style":762},[761],[572,2733,614],{"className":2734},[766],[572,2736],{"className":2737,"style":762},[761],[572,2739,611],{"className":2740},[757],[572,2742],{"className":2743,"style":762},[761],[572,2745,2747,2782],{"className":2746},[649],[572,2748,2750],{"className":2749},[649,653],[572,2751,2753],{"className":2752},[657],[572,2754,2756],{"className":2755},[661],[572,2757,2759,2767],{"className":2758,"style":666},[665],[572,2760,2761,2764],{"style":669},[572,2762],{"className":2763,"style":674},[673],[572,2765,600],{"className":2766,"style":679},[649,678],[572,2768,2769,2772],{"style":669},[572,2770],{"className":2771,"style":674},[673],[572,2773,2775],{"className":2774,"style":689},[688],[572,2776,2778],{"className":2777,"style":694},[693],[696,2779,2780],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2781],{"d":707},[572,2783,2785],{"className":2784},[711],[572,2786,2788,2808],{"className":2787},[657,715],[572,2789,2791,2805],{"className":2790},[661],[572,2792,2794],{"className":2793,"style":1680},[665],[572,2795,2796,2799],{"style":725},[572,2797],{"className":2798,"style":729},[673],[572,2800,2802],{"className":2801},[733,734,735,736],[572,2803,1524],{"className":2804,"style":1554},[649,678,736],[572,2806,744],{"className":2807},[743],[572,2809,2811],{"className":2810},[661],[572,2812,2814],{"className":2813,"style":751},[665],[572,2815],{},". Sind die ",[572,2818,2820,2841],{"className":2819},[575],[572,2821,2823],{"className":2822},[579],[581,2824,2825],{"xmlns":583},[585,2826,2827,2839],{},[588,2828,2829],{},[591,2830,2831,2837],{},[594,2832,2833,2835],{"accent":596},[598,2834,600],{},[602,2836,604],{},[598,2838,1524],{},[629,2840,1620],{"encoding":631},[572,2842,2844],{"className":2843,"ariaHidden":596},[636],[572,2845,2847,2850],{"className":2846},[640],[572,2848],{"className":2849,"style":1345},[644],[572,2851,2853,2888],{"className":2852},[649],[572,2854,2856],{"className":2855},[649,653],[572,2857,2859],{"className":2858},[657],[572,2860,2862],{"className":2861},[661],[572,2863,2865,2873],{"className":2864,"style":666},[665],[572,2866,2867,2870],{"style":669},[572,2868],{"className":2869,"style":674},[673],[572,2871,600],{"className":2872,"style":679},[649,678],[572,2874,2875,2878],{"style":669},[572,2876],{"className":2877,"style":674},[673],[572,2879,2881],{"className":2880,"style":689},[688],[572,2882,2884],{"className":2883,"style":694},[693],[696,2885,2886],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,2887],{"d":707},[572,2889,2891],{"className":2890},[711],[572,2892,2894,2914],{"className":2893},[657,715],[572,2895,2897,2911],{"className":2896},[661],[572,2898,2900],{"className":2899,"style":1680},[665],[572,2901,2902,2905],{"style":725},[572,2903],{"className":2904,"style":729},[673],[572,2906,2908],{"className":2907},[733,734,735,736],[572,2909,1524],{"className":2910,"style":1554},[649,678,736],[572,2912,744],{"className":2913},[743],[572,2915,2917],{"className":2916},[661],[572,2918,2920],{"className":2919,"style":751},[665],[572,2921],{}," linear abhängig, entsteht irgendwann ",[572,2924,2926,2957],{"className":2925},[575],[572,2927,2929],{"className":2928},[579],[581,2930,2931],{"xmlns":583},[585,2932,2933,2954],{},[588,2934,2935,2945,2947],{},[591,2936,2937,2943],{},[594,2938,2939,2941],{"accent":596},[598,2940,872],{},[602,2942,604],{},[598,2944,1524],{},[602,2946,1322],{},[594,2948,2949,2952],{"accent":596},[606,2950,2951],{},"0",[602,2953,604],{},[629,2955,2956],{"encoding":631},"\\vec u_k = \\vec 0",[572,2958,2960,3047],{"className":2959,"ariaHidden":596},[636],[572,2961,2963,2966,3038,3041,3044],{"className":2962},[640],[572,2964],{"className":2965,"style":1345},[644],[572,2967,2969,3004],{"className":2968},[649],[572,2970,2972],{"className":2971},[649,653],[572,2973,2975],{"className":2974},[657],[572,2976,2978],{"className":2977},[661],[572,2979,2981,2989],{"className":2980,"style":666},[665],[572,2982,2983,2986],{"style":669},[572,2984],{"className":2985,"style":674},[673],[572,2987,872],{"className":2988},[649,678],[572,2990,2991,2994],{"style":669},[572,2992],{"className":2993,"style":674},[673],[572,2995,2997],{"className":2996,"style":689},[688],[572,2998,3000],{"className":2999,"style":694},[693],[696,3001,3002],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,3003],{"d":707},[572,3005,3007],{"className":3006},[711],[572,3008,3010,3030],{"className":3009},[657,715],[572,3011,3013,3027],{"className":3012},[661],[572,3014,3016],{"className":3015,"style":1680},[665],[572,3017,3018,3021],{"style":957},[572,3019],{"className":3020,"style":729},[673],[572,3022,3024],{"className":3023},[733,734,735,736],[572,3025,1524],{"className":3026,"style":1554},[649,678,736],[572,3028,744],{"className":3029},[743],[572,3031,3033],{"className":3032},[661],[572,3034,3036],{"className":3035,"style":751},[665],[572,3037],{},[572,3039],{"className":3040,"style":1421},[761],[572,3042,1322],{"className":3043},[1425],[572,3045],{"className":3046,"style":1421},[761],[572,3048,3050,3054],{"className":3049},[640],[572,3051],{"className":3052,"style":3053},[644],"height:0.9274em;",[572,3055,3057],{"className":3056},[649,653],[572,3058,3060],{"className":3059},[657],[572,3061,3063],{"className":3062},[661],[572,3064,3066,3074],{"className":3065,"style":3053},[665],[572,3067,3068,3071],{"style":669},[572,3069],{"className":3070,"style":674},[673],[572,3072,2951],{"className":3073},[649],[572,3075,3077,3080],{"style":3076},"top:-3.2134em;",[572,3078],{"className":3079,"style":674},[673],[572,3081,3084],{"className":3082,"style":3083},[688],"left:-0.2355em;",[572,3085,3087],{"className":3086,"style":694},[693],[696,3088,3089],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,3090],{"d":707},", und die Division im Normierungsschritt bricht ab.",[564,3093,3094,3095,3201,3202,3288,3289,3510],{},"Man darf jedes ",[572,3096,3098,3120],{"className":3097},[575],[572,3099,3101],{"className":3100},[579],[581,3102,3103],{"xmlns":583},[585,3104,3105,3117],{},[588,3106,3107],{},[591,3108,3109,3115],{},[594,3110,3111,3113],{"accent":596},[598,3112,872],{},[602,3114,604],{},[598,3116,1524],{},[629,3118,3119],{"encoding":631},"\\vec u_k",[572,3121,3123],{"className":3122,"ariaHidden":596},[636],[572,3124,3126,3129],{"className":3125},[640],[572,3127],{"className":3128,"style":1345},[644],[572,3130,3132,3167],{"className":3131},[649],[572,3133,3135],{"className":3134},[649,653],[572,3136,3138],{"className":3137},[657],[572,3139,3141],{"className":3140},[661],[572,3142,3144,3152],{"className":3143,"style":666},[665],[572,3145,3146,3149],{"style":669},[572,3147],{"className":3148,"style":674},[673],[572,3150,872],{"className":3151},[649,678],[572,3153,3154,3157],{"style":669},[572,3155],{"className":3156,"style":674},[673],[572,3158,3160],{"className":3159,"style":689},[688],[572,3161,3163],{"className":3162,"style":694},[693],[696,3164,3165],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,3166],{"d":707},[572,3168,3170],{"className":3169},[711],[572,3171,3173,3193],{"className":3172},[657,715],[572,3174,3176,3190],{"className":3175},[661],[572,3177,3179],{"className":3178,"style":1680},[665],[572,3180,3181,3184],{"style":957},[572,3182],{"className":3183,"style":729},[673],[572,3185,3187],{"className":3186},[733,734,735,736],[572,3188,1524],{"className":3189,"style":1554},[649,678,736],[572,3191,744],{"className":3192},[743],[572,3194,3196],{"className":3195},[661],[572,3197,3199],{"className":3198,"style":751},[665],[572,3200],{}," vor dem nächsten Schritt mit einer Zahl ",[572,3203,3205,3222],{"className":3204},[575],[572,3206,3208],{"className":3207},[579],[581,3209,3210],{"xmlns":583},[585,3211,3212,3219],{},[588,3213,3214,3217],{},[602,3215,3216],{"mathvariant":2086},"≠",[606,3218,2951],{},[629,3220,3221],{"encoding":631},"\\neq 0",[572,3223,3225,3278],{"className":3224,"ariaHidden":596},[636],[572,3226,3228,3232,3275],{"className":3227},[640],[572,3229],{"className":3230,"style":3231},[644],"height:0.8889em;vertical-align:-0.1944em;",[572,3233,3235,3268,3272],{"className":3234},[1425],[572,3236,3238],{"className":3237},[1425],[572,3239,3242],{"className":3240},[649,3241],"vbox",[572,3243,3246],{"className":3244},[3245],"thinbox",[572,3247,3250,3253,3264],{"className":3248},[3249],"rlap",[572,3251],{"className":3252,"style":3231},[644],[572,3254,3257],{"className":3255},[3256],"inner",[572,3258,3260],{"className":3259},[649],[572,3261,3263],{"className":3262},[1425],"",[572,3265],{"className":3266},[3267],"fix",[572,3269],{"className":3270},[761,3271],"nobreak",[572,3273,1322],{"className":3274},[1425],[572,3276],{"className":3277,"style":1421},[761],[572,3279,3281,3285],{"className":3280},[640],[572,3282],{"className":3283,"style":3284},[644],"height:0.6444em;",[572,3286,2951],{"className":3287},[649]," multiplizieren, um Brüche zu vermeiden. Die Richtung, und damit das Ergebnis nach dem Normieren, bleibt bis aufs Vorzeichen gleich. Das Verfahren funktioniert mit jedem Skalarprodukt, z.B. auch mit ",[572,3290,3292,3362],{"className":3291},[575],[572,3293,3295],{"className":3294},[579],[581,3296,3297],{"xmlns":583},[585,3298,3299,3359],{},[588,3300,3301,3304,3307,3309,3312,3315,3317,3331,3333,3336,3339,3342,3344,3346,3348,3350,3354,3357],{},[602,3302,3303],{"stretchy":2090},"⟨",[598,3305,3306],{},"f",[602,3308,611],{"separator":596},[598,3310,3311],{},"g",[602,3313,3314],{"stretchy":2090},"⟩",[602,3316,1322],{},[3318,3319,3320,3323,3329],"msubsup",{},[602,3321,3322],{},"∫",[588,3324,3325,3327],{},[602,3326,1858],{},[606,3328,608],{},[606,3330,608],{},[598,3332,3306],{},[602,3334,3335],{"stretchy":2090},"(",[598,3337,3338],{},"x",[602,3340,3341],{"stretchy":2090},")",[598,3343,3311],{},[602,3345,3335],{"stretchy":2090},[598,3347,3338],{},[602,3349,3341],{"stretchy":2090},[3351,3352,3353],"mtext",{}," ",[598,3355,3356],{},"d",[598,3358,3338],{},[629,3360,3361],{"encoding":631},"\\langle f, g \\rangle = \\int_{-1}^{1} f(x) g(x)\\,dx",[572,3363,3365,3399],{"className":3364,"ariaHidden":596},[636],[572,3366,3368,3371,3374,3378,3381,3384,3387,3390,3393,3396],{"className":3367},[640],[572,3369],{"className":3370,"style":2203},[644],[572,3372,3303],{"className":3373},[2282],[572,3375,3306],{"className":3376,"style":3377},[649,678],"margin-right:0.1076em;",[572,3379,611],{"className":3380},[757],[572,3382],{"className":3383,"style":762},[761],[572,3385,3311],{"className":3386,"style":679},[649,678],[572,3388,3314],{"className":3389},[2358],[572,3391],{"className":3392,"style":1421},[761],[572,3394,1322],{"className":3395},[1425],[572,3397],{"className":3398,"style":1421},[761],[572,3400,3402,3406,3474,3477,3480,3483,3486,3489,3492,3495,3498,3501,3504,3507],{"className":3401},[640],[572,3403],{"className":3404,"style":3405},[644],"height:1.4232em;vertical-align:-0.4142em;",[572,3407,3410,3416],{"className":3408},[3409],"mop",[572,3411,3322],{"className":3412,"style":3415},[3409,3413,3414],"op-symbol","small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[572,3417,3419],{"className":3418},[711],[572,3420,3422,3465],{"className":3421},[657,715],[572,3423,3425,3462],{"className":3424},[661],[572,3426,3429,3447],{"className":3427,"style":3428},[665],"height:1.009em;",[572,3430,3432,3435],{"style":3431},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[572,3433],{"className":3434,"style":729},[673],[572,3436,3438],{"className":3437},[733,734,735,736],[572,3439,3441,3444],{"className":3440},[649,736],[572,3442,1858],{"className":3443},[649,736],[572,3445,608],{"className":3446},[649,736],[572,3448,3450,3453],{"style":3449},"top:-3.2579em;margin-right:0.05em;",[572,3451],{"className":3452,"style":729},[673],[572,3454,3456],{"className":3455},[733,734,735,736],[572,3457,3459],{"className":3458},[649,736],[572,3460,608],{"className":3461},[649,736],[572,3463,744],{"className":3464},[743],[572,3466,3468],{"className":3467},[661],[572,3469,3472],{"className":3470,"style":3471},[665],"height:0.4142em;",[572,3473],{},[572,3475],{"className":3476,"style":762},[761],[572,3478,3306],{"className":3479,"style":3377},[649,678],[572,3481,3335],{"className":3482},[2282],[572,3484,3338],{"className":3485},[649,678],[572,3487,3341],{"className":3488},[2358],[572,3490,3311],{"className":3491,"style":679},[649,678],[572,3493,3335],{"className":3494},[2282],[572,3496,3338],{"className":3497},[649,678],[572,3499,3341],{"className":3500},[2358],[572,3502],{"className":3503,"style":762},[761],[572,3505,3356],{"className":3506},[649,678],[572,3508,3338],{"className":3509},[649,678]," für Polynome.",[559,3512,3514],{"id":3513},"beispiele","Beispiele",[564,3516,3517,3518,3693,3694,3693,3868,1288],{},"Gegeben ",[572,3519,3521,3564],{"className":3520},[575],[572,3522,3524],{"className":3523},[579],[581,3525,3526],{"xmlns":583},[585,3527,3528,3561],{},[588,3529,3530,3540,3542,3544,3546,3548,3551,3553,3555,3557,3559],{},[591,3531,3532,3538],{},[594,3533,3534,3536],{"accent":596},[598,3535,600],{},[602,3537,604],{},[606,3539,608],{},[602,3541,1322],{},[602,3543,3335],{"stretchy":2090},[606,3545,608],{},[602,3547,611],{"separator":596},[3351,3549,3550],{}," ",[606,3552,608],{},[602,3554,611],{"separator":596},[3351,3556,3550],{},[606,3558,2951],{},[602,3560,3341],{"stretchy":2090},[629,3562,3563],{"encoding":631},"\\vec v_1 = (1,\\ 1,\\ 0)",[572,3565,3567,3654],{"className":3566,"ariaHidden":596},[636],[572,3568,3570,3573,3645,3648,3651],{"className":3569},[640],[572,3571],{"className":3572,"style":1345},[644],[572,3574,3576,3611],{"className":3575},[649],[572,3577,3579],{"className":3578},[649,653],[572,3580,3582],{"className":3581},[657],[572,3583,3585],{"className":3584},[661],[572,3586,3588,3596],{"className":3587,"style":666},[665],[572,3589,3590,3593],{"style":669},[572,3591],{"className":3592,"style":674},[673],[572,3594,600],{"className":3595,"style":679},[649,678],[572,3597,3598,3601],{"style":669},[572,3599],{"className":3600,"style":674},[673],[572,3602,3604],{"className":3603,"style":689},[688],[572,3605,3607],{"className":3606,"style":694},[693],[696,3608,3609],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,3610],{"d":707},[572,3612,3614],{"className":3613},[711],[572,3615,3617,3637],{"className":3616},[657,715],[572,3618,3620,3634],{"className":3619},[661],[572,3621,3623],{"className":3622,"style":722},[665],[572,3624,3625,3628],{"style":725},[572,3626],{"className":3627,"style":729},[673],[572,3629,3631],{"className":3630},[733,734,735,736],[572,3632,608],{"className":3633},[649,736],[572,3635,744],{"className":3636},[743],[572,3638,3640],{"className":3639},[661],[572,3641,3643],{"className":3642,"style":751},[665],[572,3644],{},[572,3646],{"className":3647,"style":1421},[761],[572,3649,1322],{"className":3650},[1425],[572,3652],{"className":3653,"style":1421},[761],[572,3655,3657,3660,3663,3666,3669,3672,3675,3678,3681,3684,3687,3690],{"className":3656},[640],[572,3658],{"className":3659,"style":2203},[644],[572,3661,3335],{"className":3662},[2282],[572,3664,608],{"className":3665},[649],[572,3667,611],{"className":3668},[757],[572,3670,3550],{"className":3671},[761],[572,3673],{"className":3674,"style":762},[761],[572,3676,608],{"className":3677},[649],[572,3679,611],{"className":3680},[757],[572,3682,3550],{"className":3683},[761],[572,3685],{"className":3686,"style":762},[761],[572,3688,2951],{"className":3689},[649],[572,3691,3341],{"className":3692},[2358],", ",[572,3695,3697,3739],{"className":3696},[575],[572,3698,3700],{"className":3699},[579],[581,3701,3702],{"xmlns":583},[585,3703,3704,3736],{},[588,3705,3706,3716,3718,3720,3722,3724,3726,3728,3730,3732,3734],{},[591,3707,3708,3714],{},[594,3709,3710,3712],{"accent":596},[598,3711,600],{},[602,3713,604],{},[606,3715,1529],{},[602,3717,1322],{},[602,3719,3335],{"stretchy":2090},[606,3721,608],{},[602,3723,611],{"separator":596},[3351,3725,3550],{},[606,3727,2951],{},[602,3729,611],{"separator":596},[3351,3731,3550],{},[606,3733,608],{},[602,3735,3341],{"stretchy":2090},[629,3737,3738],{"encoding":631},"\\vec v_2 = (1,\\ 0,\\ 1)",[572,3740,3742,3829],{"className":3741,"ariaHidden":596},[636],[572,3743,3745,3748,3820,3823,3826],{"className":3744},[640],[572,3746],{"className":3747,"style":1345},[644],[572,3749,3751,3786],{"className":3750},[649],[572,3752,3754],{"className":3753},[649,653],[572,3755,3757],{"className":3756},[657],[572,3758,3760],{"className":3759},[661],[572,3761,3763,3771],{"className":3762,"style":666},[665],[572,3764,3765,3768],{"style":669},[572,3766],{"className":3767,"style":674},[673],[572,3769,600],{"className":3770,"style":679},[649,678],[572,3772,3773,3776],{"style":669},[572,3774],{"className":3775,"style":674},[673],[572,3777,3779],{"className":3778,"style":689},[688],[572,3780,3782],{"className":3781,"style":694},[693],[696,3783,3784],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,3785],{"d":707},[572,3787,3789],{"className":3788},[711],[572,3790,3792,3812],{"className":3791},[657,715],[572,3793,3795,3809],{"className":3794},[661],[572,3796,3798],{"className":3797,"style":722},[665],[572,3799,3800,3803],{"style":725},[572,3801],{"className":3802,"style":729},[673],[572,3804,3806],{"className":3805},[733,734,735,736],[572,3807,1529],{"className":3808},[649,736],[572,3810,744],{"className":3811},[743],[572,3813,3815],{"className":3814},[661],[572,3816,3818],{"className":3817,"style":751},[665],[572,3819],{},[572,3821],{"className":3822,"style":1421},[761],[572,3824,1322],{"className":3825},[1425],[572,3827],{"className":3828,"style":1421},[761],[572,3830,3832,3835,3838,3841,3844,3847,3850,3853,3856,3859,3862,3865],{"className":3831},[640],[572,3833],{"className":3834,"style":2203},[644],[572,3836,3335],{"className":3837},[2282],[572,3839,608],{"className":3840},[649],[572,3842,611],{"className":3843},[757],[572,3845,3550],{"className":3846},[761],[572,3848],{"className":3849,"style":762},[761],[572,3851,2951],{"className":3852},[649],[572,3854,611],{"className":3855},[757],[572,3857,3550],{"className":3858},[761],[572,3860],{"className":3861,"style":762},[761],[572,3863,608],{"className":3864},[649],[572,3866,3341],{"className":3867},[2358],[572,3869,3871,3914],{"className":3870},[575],[572,3872,3874],{"className":3873},[579],[581,3875,3876],{"xmlns":583},[585,3877,3878,3911],{},[588,3879,3880,3891,3893,3895,3897,3899,3901,3903,3905,3907,3909],{},[591,3881,3882,3888],{},[594,3883,3884,3886],{"accent":596},[598,3885,600],{},[602,3887,604],{},[606,3889,3890],{},"3",[602,3892,1322],{},[602,3894,3335],{"stretchy":2090},[606,3896,2951],{},[602,3898,611],{"separator":596},[3351,3900,3550],{},[606,3902,608],{},[602,3904,611],{"separator":596},[3351,3906,3550],{},[606,3908,608],{},[602,3910,3341],{"stretchy":2090},[629,3912,3913],{"encoding":631},"\\vec v_3 = (0,\\ 1,\\ 1)",[572,3915,3917,4004],{"className":3916,"ariaHidden":596},[636],[572,3918,3920,3923,3995,3998,4001],{"className":3919},[640],[572,3921],{"className":3922,"style":1345},[644],[572,3924,3926,3961],{"className":3925},[649],[572,3927,3929],{"className":3928},[649,653],[572,3930,3932],{"className":3931},[657],[572,3933,3935],{"className":3934},[661],[572,3936,3938,3946],{"className":3937,"style":666},[665],[572,3939,3940,3943],{"style":669},[572,3941],{"className":3942,"style":674},[673],[572,3944,600],{"className":3945,"style":679},[649,678],[572,3947,3948,3951],{"style":669},[572,3949],{"className":3950,"style":674},[673],[572,3952,3954],{"className":3953,"style":689},[688],[572,3955,3957],{"className":3956,"style":694},[693],[696,3958,3959],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,3960],{"d":707},[572,3962,3964],{"className":3963},[711],[572,3965,3967,3987],{"className":3966},[657,715],[572,3968,3970,3984],{"className":3969},[661],[572,3971,3973],{"className":3972,"style":722},[665],[572,3974,3975,3978],{"style":725},[572,3976],{"className":3977,"style":729},[673],[572,3979,3981],{"className":3980},[733,734,735,736],[572,3982,3890],{"className":3983},[649,736],[572,3985,744],{"className":3986},[743],[572,3988,3990],{"className":3989},[661],[572,3991,3993],{"className":3992,"style":751},[665],[572,3994],{},[572,3996],{"className":3997,"style":1421},[761],[572,3999,1322],{"className":4000},[1425],[572,4002],{"className":4003,"style":1421},[761],[572,4005,4007,4010,4013,4016,4019,4022,4025,4028,4031,4034,4037,4040],{"className":4006},[640],[572,4008],{"className":4009,"style":2203},[644],[572,4011,3335],{"className":4012},[2282],[572,4014,2951],{"className":4015},[649],[572,4017,611],{"className":4018},[757],[572,4020,3550],{"className":4021},[761],[572,4023],{"className":4024,"style":762},[761],[572,4026,608],{"className":4027},[649],[572,4029,611],{"className":4030},[757],[572,4032,3550],{"className":4033},[761],[572,4035],{"className":4036,"style":762},[761],[572,4038,608],{"className":4039},[649],[572,4041,3341],{"className":4042},[2358],[564,4044,4045,3693,4219,1288],{},[572,4046,4048,4090],{"className":4047},[575],[572,4049,4051],{"className":4050},[579],[581,4052,4053],{"xmlns":583},[585,4054,4055,4087],{},[588,4056,4057,4067,4069,4071,4073,4075,4077,4079,4081,4083,4085],{},[591,4058,4059,4065],{},[594,4060,4061,4063],{"accent":596},[598,4062,872],{},[602,4064,604],{},[606,4066,608],{},[602,4068,1322],{},[602,4070,3335],{"stretchy":2090},[606,4072,608],{},[602,4074,611],{"separator":596},[3351,4076,3550],{},[606,4078,608],{},[602,4080,611],{"separator":596},[3351,4082,3550],{},[606,4084,2951],{},[602,4086,3341],{"stretchy":2090},[629,4088,4089],{"encoding":631},"\\vec u_1 = (1,\\ 1,\\ 0)",[572,4091,4093,4180],{"className":4092,"ariaHidden":596},[636],[572,4094,4096,4099,4171,4174,4177],{"className":4095},[640],[572,4097],{"className":4098,"style":1345},[644],[572,4100,4102,4137],{"className":4101},[649],[572,4103,4105],{"className":4104},[649,653],[572,4106,4108],{"className":4107},[657],[572,4109,4111],{"className":4110},[661],[572,4112,4114,4122],{"className":4113,"style":666},[665],[572,4115,4116,4119],{"style":669},[572,4117],{"className":4118,"style":674},[673],[572,4120,872],{"className":4121},[649,678],[572,4123,4124,4127],{"style":669},[572,4125],{"className":4126,"style":674},[673],[572,4128,4130],{"className":4129,"style":689},[688],[572,4131,4133],{"className":4132,"style":694},[693],[696,4134,4135],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4136],{"d":707},[572,4138,4140],{"className":4139},[711],[572,4141,4143,4163],{"className":4142},[657,715],[572,4144,4146,4160],{"className":4145},[661],[572,4147,4149],{"className":4148,"style":722},[665],[572,4150,4151,4154],{"style":957},[572,4152],{"className":4153,"style":729},[673],[572,4155,4157],{"className":4156},[733,734,735,736],[572,4158,608],{"className":4159},[649,736],[572,4161,744],{"className":4162},[743],[572,4164,4166],{"className":4165},[661],[572,4167,4169],{"className":4168,"style":751},[665],[572,4170],{},[572,4172],{"className":4173,"style":1421},[761],[572,4175,1322],{"className":4176},[1425],[572,4178],{"className":4179,"style":1421},[761],[572,4181,4183,4186,4189,4192,4195,4198,4201,4204,4207,4210,4213,4216],{"className":4182},[640],[572,4184],{"className":4185,"style":2203},[644],[572,4187,3335],{"className":4188},[2282],[572,4190,608],{"className":4191},[649],[572,4193,611],{"className":4194},[757],[572,4196,3550],{"className":4197},[761],[572,4199],{"className":4200,"style":762},[761],[572,4202,608],{"className":4203},[649],[572,4205,611],{"className":4206},[757],[572,4208,3550],{"className":4209},[761],[572,4211],{"className":4212,"style":762},[761],[572,4214,2951],{"className":4215},[649],[572,4217,3341],{"className":4218},[2358],[572,4220,4222,4264],{"className":4221},[575],[572,4223,4225],{"className":4224},[579],[581,4226,4227],{"xmlns":583},[585,4228,4229,4261],{},[588,4230,4231,4233,4243,4245,4255,4257,4259],{},[602,4232,3303],{"stretchy":2090},[591,4234,4235,4241],{},[594,4236,4237,4239],{"accent":596},[598,4238,872],{},[602,4240,604],{},[606,4242,608],{},[602,4244,611],{"separator":596},[591,4246,4247,4253],{},[594,4248,4249,4251],{"accent":596},[598,4250,872],{},[602,4252,604],{},[606,4254,608],{},[602,4256,3314],{"stretchy":2090},[602,4258,1322],{},[606,4260,1529],{},[629,4262,4263],{"encoding":631},"\\langle \\vec u_1, \\vec u_1 \\rangle = 2",[572,4265,4267,4438],{"className":4266,"ariaHidden":596},[636],[572,4268,4270,4273,4276,4348,4351,4354,4426,4429,4432,4435],{"className":4269},[640],[572,4271],{"className":4272,"style":2203},[644],[572,4274,3303],{"className":4275},[2282],[572,4277,4279,4314],{"className":4278},[649],[572,4280,4282],{"className":4281},[649,653],[572,4283,4285],{"className":4284},[657],[572,4286,4288],{"className":4287},[661],[572,4289,4291,4299],{"className":4290,"style":666},[665],[572,4292,4293,4296],{"style":669},[572,4294],{"className":4295,"style":674},[673],[572,4297,872],{"className":4298},[649,678],[572,4300,4301,4304],{"style":669},[572,4302],{"className":4303,"style":674},[673],[572,4305,4307],{"className":4306,"style":689},[688],[572,4308,4310],{"className":4309,"style":694},[693],[696,4311,4312],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4313],{"d":707},[572,4315,4317],{"className":4316},[711],[572,4318,4320,4340],{"className":4319},[657,715],[572,4321,4323,4337],{"className":4322},[661],[572,4324,4326],{"className":4325,"style":722},[665],[572,4327,4328,4331],{"style":957},[572,4329],{"className":4330,"style":729},[673],[572,4332,4334],{"className":4333},[733,734,735,736],[572,4335,608],{"className":4336},[649,736],[572,4338,744],{"className":4339},[743],[572,4341,4343],{"className":4342},[661],[572,4344,4346],{"className":4345,"style":751},[665],[572,4347],{},[572,4349,611],{"className":4350},[757],[572,4352],{"className":4353,"style":762},[761],[572,4355,4357,4392],{"className":4356},[649],[572,4358,4360],{"className":4359},[649,653],[572,4361,4363],{"className":4362},[657],[572,4364,4366],{"className":4365},[661],[572,4367,4369,4377],{"className":4368,"style":666},[665],[572,4370,4371,4374],{"style":669},[572,4372],{"className":4373,"style":674},[673],[572,4375,872],{"className":4376},[649,678],[572,4378,4379,4382],{"style":669},[572,4380],{"className":4381,"style":674},[673],[572,4383,4385],{"className":4384,"style":689},[688],[572,4386,4388],{"className":4387,"style":694},[693],[696,4389,4390],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4391],{"d":707},[572,4393,4395],{"className":4394},[711],[572,4396,4398,4418],{"className":4397},[657,715],[572,4399,4401,4415],{"className":4400},[661],[572,4402,4404],{"className":4403,"style":722},[665],[572,4405,4406,4409],{"style":957},[572,4407],{"className":4408,"style":729},[673],[572,4410,4412],{"className":4411},[733,734,735,736],[572,4413,608],{"className":4414},[649,736],[572,4416,744],{"className":4417},[743],[572,4419,4421],{"className":4420},[661],[572,4422,4424],{"className":4423,"style":751},[665],[572,4425],{},[572,4427,3314],{"className":4428},[2358],[572,4430],{"className":4431,"style":1421},[761],[572,4433,1322],{"className":4434},[1425],[572,4436],{"className":4437,"style":1421},[761],[572,4439,4441,4444],{"className":4440},[640],[572,4442],{"className":4443,"style":3284},[644],[572,4445,1529],{"className":4446},[649],[564,4448,4449,3693,5070,1288],{},[572,4450,4452,4542],{"className":4451},[575],[572,4453,4455],{"className":4454},[579],[581,4456,4457],{"xmlns":583},[585,4458,4459,4539],{},[588,4460,4461,4471,4473,4483,4485,4492,4502,4504],{},[591,4462,4463,4469],{},[594,4464,4465,4467],{"accent":596},[598,4466,872],{},[602,4468,604],{},[606,4470,1529],{},[602,4472,1322],{},[591,4474,4475,4481],{},[594,4476,4477,4479],{"accent":596},[598,4478,600],{},[602,4480,604],{},[606,4482,1529],{},[602,4484,1858],{},[4486,4487,4488,4490],"mfrac",{},[606,4489,608],{},[606,4491,1529],{},[591,4493,4494,4500],{},[594,4495,4496,4498],{"accent":596},[598,4497,872],{},[602,4499,604],{},[606,4501,608],{},[602,4503,1322],{},[588,4505,4506,4508,4517,4519,4521,4523,4531,4533,4535,4537],{},[602,4507,3335],{"fence":596},[4509,4510,4511],"mstyle",{"scriptlevel":2951,"displaystyle":2090},[4486,4512,4513,4515],{},[606,4514,608],{},[606,4516,1529],{},[602,4518,611],{"separator":596},[3351,4520,3550],{},[602,4522,1858],{},[4509,4524,4525],{"scriptlevel":2951,"displaystyle":2090},[4486,4526,4527,4529],{},[606,4528,608],{},[606,4530,1529],{},[602,4532,611],{"separator":596},[3351,4534,3550],{},[606,4536,608],{},[602,4538,3341],{"fence":596},[629,4540,4541],{"encoding":631},"\\vec u_2 = \\vec v_2 - \\frac{1}{2}\\vec u_1 = \\left(\\tfrac12,\\ -\\tfrac12,\\ 1\\right)",[572,4543,4545,4632,4720,4884],{"className":4544,"ariaHidden":596},[636],[572,4546,4548,4551,4623,4626,4629],{"className":4547},[640],[572,4549],{"className":4550,"style":1345},[644],[572,4552,4554,4589],{"className":4553},[649],[572,4555,4557],{"className":4556},[649,653],[572,4558,4560],{"className":4559},[657],[572,4561,4563],{"className":4562},[661],[572,4564,4566,4574],{"className":4565,"style":666},[665],[572,4567,4568,4571],{"style":669},[572,4569],{"className":4570,"style":674},[673],[572,4572,872],{"className":4573},[649,678],[572,4575,4576,4579],{"style":669},[572,4577],{"className":4578,"style":674},[673],[572,4580,4582],{"className":4581,"style":689},[688],[572,4583,4585],{"className":4584,"style":694},[693],[696,4586,4587],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4588],{"d":707},[572,4590,4592],{"className":4591},[711],[572,4593,4595,4615],{"className":4594},[657,715],[572,4596,4598,4612],{"className":4597},[661],[572,4599,4601],{"className":4600,"style":722},[665],[572,4602,4603,4606],{"style":957},[572,4604],{"className":4605,"style":729},[673],[572,4607,4609],{"className":4608},[733,734,735,736],[572,4610,1529],{"className":4611},[649,736],[572,4613,744],{"className":4614},[743],[572,4616,4618],{"className":4617},[661],[572,4619,4621],{"className":4620,"style":751},[665],[572,4622],{},[572,4624],{"className":4625,"style":1421},[761],[572,4627,1322],{"className":4628},[1425],[572,4630],{"className":4631,"style":1421},[761],[572,4633,4635,4638,4710,4714,4717],{"className":4634},[640],[572,4636],{"className":4637,"style":1345},[644],[572,4639,4641,4676],{"className":4640},[649],[572,4642,4644],{"className":4643},[649,653],[572,4645,4647],{"className":4646},[657],[572,4648,4650],{"className":4649},[661],[572,4651,4653,4661],{"className":4652,"style":666},[665],[572,4654,4655,4658],{"style":669},[572,4656],{"className":4657,"style":674},[673],[572,4659,600],{"className":4660,"style":679},[649,678],[572,4662,4663,4666],{"style":669},[572,4664],{"className":4665,"style":674},[673],[572,4667,4669],{"className":4668,"style":689},[688],[572,4670,4672],{"className":4671,"style":694},[693],[696,4673,4674],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4675],{"d":707},[572,4677,4679],{"className":4678},[711],[572,4680,4682,4702],{"className":4681},[657,715],[572,4683,4685,4699],{"className":4684},[661],[572,4686,4688],{"className":4687,"style":722},[665],[572,4689,4690,4693],{"style":725},[572,4691],{"className":4692,"style":729},[673],[572,4694,4696],{"className":4695},[733,734,735,736],[572,4697,1529],{"className":4698},[649,736],[572,4700,744],{"className":4701},[743],[572,4703,4705],{"className":4704},[661],[572,4706,4708],{"className":4707,"style":751},[665],[572,4709],{},[572,4711],{"className":4712,"style":4713},[761],"margin-right:0.2222em;",[572,4715,1858],{"className":4716},[2031],[572,4718],{"className":4719,"style":4713},[761],[572,4721,4723,4727,4803,4875,4878,4881],{"className":4722},[640],[572,4724],{"className":4725,"style":4726},[644],"height:1.1901em;vertical-align:-0.345em;",[572,4728,4730,4734,4800],{"className":4729},[649],[572,4731],{"className":4732},[2282,4733],"nulldelimiter",[572,4735,4737],{"className":4736},[4486],[572,4738,4740,4791],{"className":4739},[657,715],[572,4741,4743,4788],{"className":4742},[661],[572,4744,4747,4762,4773],{"className":4745,"style":4746},[665],"height:0.8451em;",[572,4748,4750,4753],{"style":4749},"top:-2.655em;",[572,4751],{"className":4752,"style":674},[673],[572,4754,4756],{"className":4755},[733,734,735,736],[572,4757,4759],{"className":4758},[649,736],[572,4760,1529],{"className":4761},[649,736],[572,4763,4765,4768],{"style":4764},"top:-3.23em;",[572,4766],{"className":4767,"style":674},[673],[572,4769],{"className":4770,"style":4772},[4771],"frac-line","border-bottom-width:0.04em;",[572,4774,4776,4779],{"style":4775},"top:-3.394em;",[572,4777],{"className":4778,"style":674},[673],[572,4780,4782],{"className":4781},[733,734,735,736],[572,4783,4785],{"className":4784},[649,736],[572,4786,608],{"className":4787},[649,736],[572,4789,744],{"className":4790},[743],[572,4792,4794],{"className":4793},[661],[572,4795,4798],{"className":4796,"style":4797},[665],"height:0.345em;",[572,4799],{},[572,4801],{"className":4802},[2358,4733],[572,4804,4806,4841],{"className":4805},[649],[572,4807,4809],{"className":4808},[649,653],[572,4810,4812],{"className":4811},[657],[572,4813,4815],{"className":4814},[661],[572,4816,4818,4826],{"className":4817,"style":666},[665],[572,4819,4820,4823],{"style":669},[572,4821],{"className":4822,"style":674},[673],[572,4824,872],{"className":4825},[649,678],[572,4827,4828,4831],{"style":669},[572,4829],{"className":4830,"style":674},[673],[572,4832,4834],{"className":4833,"style":689},[688],[572,4835,4837],{"className":4836,"style":694},[693],[696,4838,4839],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,4840],{"d":707},[572,4842,4844],{"className":4843},[711],[572,4845,4847,4867],{"className":4846},[657,715],[572,4848,4850,4864],{"className":4849},[661],[572,4851,4853],{"className":4852,"style":722},[665],[572,4854,4855,4858],{"style":957},[572,4856],{"className":4857,"style":729},[673],[572,4859,4861],{"className":4860},[733,734,735,736],[572,4862,608],{"className":4863},[649,736],[572,4865,744],{"className":4866},[743],[572,4868,4870],{"className":4869},[661],[572,4871,4873],{"className":4872,"style":751},[665],[572,4874],{},[572,4876],{"className":4877,"style":1421},[761],[572,4879,1322],{"className":4880},[1425],[572,4882],{"className":4883,"style":1421},[761],[572,4885,4887,4891],{"className":4886},[640],[572,4888],{"className":4889,"style":4890},[644],"height:1.2em;vertical-align:-0.35em;",[572,4892,4894,4904,4972,4975,4978,4981,4984,5052,5055,5058,5061,5064],{"className":4893},[766],[572,4895,4899],{"className":4896,"style":4898},[2282,4897],"delimcenter","top:0em;",[572,4900,3335],{"className":4901},[4902,4903],"delimsizing","size1",[572,4905,4907,4910,4969],{"className":4906},[649],[572,4908],{"className":4909},[2282,4733],[572,4911,4913],{"className":4912},[4486],[572,4914,4916,4961],{"className":4915},[657,715],[572,4917,4919,4958],{"className":4918},[661],[572,4920,4922,4936,4944],{"className":4921,"style":4746},[665],[572,4923,4924,4927],{"style":4749},[572,4925],{"className":4926,"style":674},[673],[572,4928,4930],{"className":4929},[733,734,735,736],[572,4931,4933],{"className":4932},[649,736],[572,4934,1529],{"className":4935},[649,736],[572,4937,4938,4941],{"style":4764},[572,4939],{"className":4940,"style":674},[673],[572,4942],{"className":4943,"style":4772},[4771],[572,4945,4946,4949],{"style":4775},[572,4947],{"className":4948,"style":674},[673],[572,4950,4952],{"className":4951},[733,734,735,736],[572,4953,4955],{"className":4954},[649,736],[572,4956,608],{"className":4957},[649,736],[572,4959,744],{"className":4960},[743],[572,4962,4964],{"className":4963},[661],[572,4965,4967],{"className":4966,"style":4797},[665],[572,4968],{},[572,4970],{"className":4971},[2358,4733],[572,4973,611],{"className":4974},[757],[572,4976,3550],{"className":4977},[761],[572,4979],{"className":4980,"style":762},[761],[572,4982,1858],{"className":4983},[649],[572,4985,4987,4990,5049],{"className":4986},[649],[572,4988],{"className":4989},[2282,4733],[572,4991,4993],{"className":4992},[4486],[572,4994,4996,5041],{"className":4995},[657,715],[572,4997,4999,5038],{"className":4998},[661],[572,5000,5002,5016,5024],{"className":5001,"style":4746},[665],[572,5003,5004,5007],{"style":4749},[572,5005],{"className":5006,"style":674},[673],[572,5008,5010],{"className":5009},[733,734,735,736],[572,5011,5013],{"className":5012},[649,736],[572,5014,1529],{"className":5015},[649,736],[572,5017,5018,5021],{"style":4764},[572,5019],{"className":5020,"style":674},[673],[572,5022],{"className":5023,"style":4772},[4771],[572,5025,5026,5029],{"style":4775},[572,5027],{"className":5028,"style":674},[673],[572,5030,5032],{"className":5031},[733,734,735,736],[572,5033,5035],{"className":5034},[649,736],[572,5036,608],{"className":5037},[649,736],[572,5039,744],{"className":5040},[743],[572,5042,5044],{"className":5043},[661],[572,5045,5047],{"className":5046,"style":4797},[665],[572,5048],{},[572,5050],{"className":5051},[2358,4733],[572,5053,611],{"className":5054},[757],[572,5056,3550],{"className":5057},[761],[572,5059],{"className":5060,"style":762},[761],[572,5062,608],{"className":5063},[649],[572,5065,5067],{"className":5066,"style":4898},[2358,4897],[572,5068,3341],{"className":5069},[4902,4903],[572,5071,5073,5119],{"className":5072},[575],[572,5074,5076],{"className":5075},[579],[581,5077,5078],{"xmlns":583},[585,5079,5080,5116],{},[588,5081,5082,5084,5094,5096,5106,5108,5110],{},[602,5083,3303],{"stretchy":2090},[591,5085,5086,5092],{},[594,5087,5088,5090],{"accent":596},[598,5089,872],{},[602,5091,604],{},[606,5093,1529],{},[602,5095,611],{"separator":596},[591,5097,5098,5104],{},[594,5099,5100,5102],{"accent":596},[598,5101,872],{},[602,5103,604],{},[606,5105,1529],{},[602,5107,3314],{"stretchy":2090},[602,5109,1322],{},[4486,5111,5112,5114],{},[606,5113,3890],{},[606,5115,1529],{},[629,5117,5118],{"encoding":631},"\\langle \\vec u_2, \\vec u_2 \\rangle = \\frac{3}{2}",[572,5120,5122,5293],{"className":5121,"ariaHidden":596},[636],[572,5123,5125,5128,5131,5203,5206,5209,5281,5284,5287,5290],{"className":5124},[640],[572,5126],{"className":5127,"style":2203},[644],[572,5129,3303],{"className":5130},[2282],[572,5132,5134,5169],{"className":5133},[649],[572,5135,5137],{"className":5136},[649,653],[572,5138,5140],{"className":5139},[657],[572,5141,5143],{"className":5142},[661],[572,5144,5146,5154],{"className":5145,"style":666},[665],[572,5147,5148,5151],{"style":669},[572,5149],{"className":5150,"style":674},[673],[572,5152,872],{"className":5153},[649,678],[572,5155,5156,5159],{"style":669},[572,5157],{"className":5158,"style":674},[673],[572,5160,5162],{"className":5161,"style":689},[688],[572,5163,5165],{"className":5164,"style":694},[693],[696,5166,5167],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,5168],{"d":707},[572,5170,5172],{"className":5171},[711],[572,5173,5175,5195],{"className":5174},[657,715],[572,5176,5178,5192],{"className":5177},[661],[572,5179,5181],{"className":5180,"style":722},[665],[572,5182,5183,5186],{"style":957},[572,5184],{"className":5185,"style":729},[673],[572,5187,5189],{"className":5188},[733,734,735,736],[572,5190,1529],{"className":5191},[649,736],[572,5193,744],{"className":5194},[743],[572,5196,5198],{"className":5197},[661],[572,5199,5201],{"className":5200,"style":751},[665],[572,5202],{},[572,5204,611],{"className":5205},[757],[572,5207],{"className":5208,"style":762},[761],[572,5210,5212,5247],{"className":5211},[649],[572,5213,5215],{"className":5214},[649,653],[572,5216,5218],{"className":5217},[657],[572,5219,5221],{"className":5220},[661],[572,5222,5224,5232],{"className":5223,"style":666},[665],[572,5225,5226,5229],{"style":669},[572,5227],{"className":5228,"style":674},[673],[572,5230,872],{"className":5231},[649,678],[572,5233,5234,5237],{"style":669},[572,5235],{"className":5236,"style":674},[673],[572,5238,5240],{"className":5239,"style":689},[688],[572,5241,5243],{"className":5242,"style":694},[693],[696,5244,5245],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,5246],{"d":707},[572,5248,5250],{"className":5249},[711],[572,5251,5253,5273],{"className":5252},[657,715],[572,5254,5256,5270],{"className":5255},[661],[572,5257,5259],{"className":5258,"style":722},[665],[572,5260,5261,5264],{"style":957},[572,5262],{"className":5263,"style":729},[673],[572,5265,5267],{"className":5266},[733,734,735,736],[572,5268,1529],{"className":5269},[649,736],[572,5271,744],{"className":5272},[743],[572,5274,5276],{"className":5275},[661],[572,5277,5279],{"className":5278,"style":751},[665],[572,5280],{},[572,5282,3314],{"className":5283},[2358],[572,5285],{"className":5286,"style":1421},[761],[572,5288,1322],{"className":5289},[1425],[572,5291],{"className":5292,"style":1421},[761],[572,5294,5296,5299],{"className":5295},[640],[572,5297],{"className":5298,"style":4726},[644],[572,5300,5302,5305,5364],{"className":5301},[649],[572,5303],{"className":5304},[2282,4733],[572,5306,5308],{"className":5307},[4486],[572,5309,5311,5356],{"className":5310},[657,715],[572,5312,5314,5353],{"className":5313},[661],[572,5315,5317,5331,5339],{"className":5316,"style":4746},[665],[572,5318,5319,5322],{"style":4749},[572,5320],{"className":5321,"style":674},[673],[572,5323,5325],{"className":5324},[733,734,735,736],[572,5326,5328],{"className":5327},[649,736],[572,5329,1529],{"className":5330},[649,736],[572,5332,5333,5336],{"style":4764},[572,5334],{"className":5335,"style":674},[673],[572,5337],{"className":5338,"style":4772},[4771],[572,5340,5341,5344],{"style":4775},[572,5342],{"className":5343,"style":674},[673],[572,5345,5347],{"className":5346},[733,734,735,736],[572,5348,5350],{"className":5349},[649,736],[572,5351,3890],{"className":5352},[649,736],[572,5354,744],{"className":5355},[743],[572,5357,5359],{"className":5358},[661],[572,5360,5362],{"className":5361,"style":4797},[665],[572,5363],{},[572,5365],{"className":5366},[2358,4733],[564,5368,5369,1288],{},[572,5370,5372,5544],{"className":5371},[575],[572,5373,5375],{"className":5374},[579],[581,5376,5377],{"xmlns":583},[585,5378,5379,5541],{},[588,5380,5381,5391,5393,5403,5405,5411,5421,5423,5441,5451,5453,5463,5465,5471,5481,5483,5489,5499,5501],{},[591,5382,5383,5389],{},[594,5384,5385,5387],{"accent":596},[598,5386,872],{},[602,5388,604],{},[606,5390,3890],{},[602,5392,1322],{},[591,5394,5395,5401],{},[594,5396,5397,5399],{"accent":596},[598,5398,600],{},[602,5400,604],{},[606,5402,3890],{},[602,5404,1858],{},[4486,5406,5407,5409],{},[606,5408,608],{},[606,5410,1529],{},[591,5412,5413,5419],{},[594,5414,5415,5417],{"accent":596},[598,5416,872],{},[602,5418,604],{},[606,5420,608],{},[602,5422,1858],{},[4486,5424,5425,5433],{},[588,5426,5427,5429,5431],{},[606,5428,608],{},[598,5430,2087],{"mathvariant":2086},[606,5432,1529],{},[588,5434,5435,5437,5439],{},[606,5436,3890],{},[598,5438,2087],{"mathvariant":2086},[606,5440,1529],{},[591,5442,5443,5449],{},[594,5444,5445,5447],{"accent":596},[598,5446,872],{},[602,5448,604],{},[606,5450,1529],{},[602,5452,1322],{},[591,5454,5455,5461],{},[594,5456,5457,5459],{"accent":596},[598,5458,600],{},[602,5460,604],{},[606,5462,3890],{},[602,5464,1858],{},[4486,5466,5467,5469],{},[606,5468,608],{},[606,5470,1529],{},[591,5472,5473,5479],{},[594,5474,5475,5477],{"accent":596},[598,5476,872],{},[602,5478,604],{},[606,5480,608],{},[602,5482,1858],{},[4486,5484,5485,5487],{},[606,5486,608],{},[606,5488,3890],{},[591,5490,5491,5497],{},[594,5492,5493,5495],{"accent":596},[598,5494,872],{},[602,5496,604],{},[606,5498,1529],{},[602,5500,1322],{},[588,5502,5503,5505,5507,5515,5517,5519,5527,5529,5531,5539],{},[602,5504,3335],{"fence":596},[602,5506,1858],{},[4509,5508,5509],{"scriptlevel":2951,"displaystyle":2090},[4486,5510,5511,5513],{},[606,5512,1529],{},[606,5514,3890],{},[602,5516,611],{"separator":596},[3351,5518,3550],{},[4509,5520,5521],{"scriptlevel":2951,"displaystyle":2090},[4486,5522,5523,5525],{},[606,5524,1529],{},[606,5526,3890],{},[602,5528,611],{"separator":596},[3351,5530,3550],{},[4509,5532,5533],{"scriptlevel":2951,"displaystyle":2090},[4486,5534,5535,5537],{},[606,5536,1529],{},[606,5538,3890],{},[602,5540,3341],{"fence":596},[629,5542,5543],{"encoding":631},"\\vec u_3 = \\vec v_3 - \\frac{1}{2}\\vec u_1 - \\frac{1\u002F2}{3\u002F2}\\vec u_2 = \\vec v_3 - \\frac12 \\vec u_1 - \\frac13 \\vec u_2 = \\left(-\\tfrac23,\\ \\tfrac23,\\ \\tfrac23\\right)",[572,5545,5547,5634,5721,5876,6037,6124,6279,6434],{"className":5546,"ariaHidden":596},[636],[572,5548,5550,5553,5625,5628,5631],{"className":5549},[640],[572,5551],{"className":5552,"style":1345},[644],[572,5554,5556,5591],{"className":5555},[649],[572,5557,5559],{"className":5558},[649,653],[572,5560,5562],{"className":5561},[657],[572,5563,5565],{"className":5564},[661],[572,5566,5568,5576],{"className":5567,"style":666},[665],[572,5569,5570,5573],{"style":669},[572,5571],{"className":5572,"style":674},[673],[572,5574,872],{"className":5575},[649,678],[572,5577,5578,5581],{"style":669},[572,5579],{"className":5580,"style":674},[673],[572,5582,5584],{"className":5583,"style":689},[688],[572,5585,5587],{"className":5586,"style":694},[693],[696,5588,5589],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,5590],{"d":707},[572,5592,5594],{"className":5593},[711],[572,5595,5597,5617],{"className":5596},[657,715],[572,5598,5600,5614],{"className":5599},[661],[572,5601,5603],{"className":5602,"style":722},[665],[572,5604,5605,5608],{"style":957},[572,5606],{"className":5607,"style":729},[673],[572,5609,5611],{"className":5610},[733,734,735,736],[572,5612,3890],{"className":5613},[649,736],[572,5615,744],{"className":5616},[743],[572,5618,5620],{"className":5619},[661],[572,5621,5623],{"className":5622,"style":751},[665],[572,5624],{},[572,5626],{"className":5627,"style":1421},[761],[572,5629,1322],{"className":5630},[1425],[572,5632],{"className":5633,"style":1421},[761],[572,5635,5637,5640,5712,5715,5718],{"className":5636},[640],[572,5638],{"className":5639,"style":1345},[644],[572,5641,5643,5678],{"className":5642},[649],[572,5644,5646],{"className":5645},[649,653],[572,5647,5649],{"className":5648},[657],[572,5650,5652],{"className":5651},[661],[572,5653,5655,5663],{"className":5654,"style":666},[665],[572,5656,5657,5660],{"style":669},[572,5658],{"className":5659,"style":674},[673],[572,5661,600],{"className":5662,"style":679},[649,678],[572,5664,5665,5668],{"style":669},[572,5666],{"className":5667,"style":674},[673],[572,5669,5671],{"className":5670,"style":689},[688],[572,5672,5674],{"className":5673,"style":694},[693],[696,5675,5676],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,5677],{"d":707},[572,5679,5681],{"className":5680},[711],[572,5682,5684,5704],{"className":5683},[657,715],[572,5685,5687,5701],{"className":5686},[661],[572,5688,5690],{"className":5689,"style":722},[665],[572,5691,5692,5695],{"style":725},[572,5693],{"className":5694,"style":729},[673],[572,5696,5698],{"className":5697},[733,734,735,736],[572,5699,3890],{"className":5700},[649,736],[572,5702,744],{"className":5703},[743],[572,5705,5707],{"className":5706},[661],[572,5708,5710],{"className":5709,"style":751},[665],[572,5711],{},[572,5713],{"className":5714,"style":4713},[761],[572,5716,1858],{"className":5717},[2031],[572,5719],{"className":5720,"style":4713},[761],[572,5722,5724,5727,5795,5867,5870,5873],{"className":5723},[640],[572,5725],{"className":5726,"style":4726},[644],[572,5728,5730,5733,5792],{"className":5729},[649],[572,5731],{"className":5732},[2282,4733],[572,5734,5736],{"className":5735},[4486],[572,5737,5739,5784],{"className":5738},[657,715],[572,5740,5742,5781],{"className":5741},[661],[572,5743,5745,5759,5767],{"className":5744,"style":4746},[665],[572,5746,5747,5750],{"style":4749},[572,5748],{"className":5749,"style":674},[673],[572,5751,5753],{"className":5752},[733,734,735,736],[572,5754,5756],{"className":5755},[649,736],[572,5757,1529],{"className":5758},[649,736],[572,5760,5761,5764],{"style":4764},[572,5762],{"className":5763,"style":674},[673],[572,5765],{"className":5766,"style":4772},[4771],[572,5768,5769,5772],{"style":4775},[572,5770],{"className":5771,"style":674},[673],[572,5773,5775],{"className":5774},[733,734,735,736],[572,5776,5778],{"className":5777},[649,736],[572,5779,608],{"className":5780},[649,736],[572,5782,744],{"className":5783},[743],[572,5785,5787],{"className":5786},[661],[572,5788,5790],{"className":5789,"style":4797},[665],[572,5791],{},[572,5793],{"className":5794},[2358,4733],[572,5796,5798,5833],{"className":5797},[649],[572,5799,5801],{"className":5800},[649,653],[572,5802,5804],{"className":5803},[657],[572,5805,5807],{"className":5806},[661],[572,5808,5810,5818],{"className":5809,"style":666},[665],[572,5811,5812,5815],{"style":669},[572,5813],{"className":5814,"style":674},[673],[572,5816,872],{"className":5817},[649,678],[572,5819,5820,5823],{"style":669},[572,5821],{"className":5822,"style":674},[673],[572,5824,5826],{"className":5825,"style":689},[688],[572,5827,5829],{"className":5828,"style":694},[693],[696,5830,5831],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,5832],{"d":707},[572,5834,5836],{"className":5835},[711],[572,5837,5839,5859],{"className":5838},[657,715],[572,5840,5842,5856],{"className":5841},[661],[572,5843,5845],{"className":5844,"style":722},[665],[572,5846,5847,5850],{"style":957},[572,5848],{"className":5849,"style":729},[673],[572,5851,5853],{"className":5852},[733,734,735,736],[572,5854,608],{"className":5855},[649,736],[572,5857,744],{"className":5858},[743],[572,5860,5862],{"className":5861},[661],[572,5863,5865],{"className":5864,"style":751},[665],[572,5866],{},[572,5868],{"className":5869,"style":4713},[761],[572,5871,1858],{"className":5872},[2031],[572,5874],{"className":5875,"style":4713},[761],[572,5877,5879,5883,5956,6028,6031,6034],{"className":5878},[640],[572,5880],{"className":5881,"style":5882},[644],"height:1.53em;vertical-align:-0.52em;",[572,5884,5886,5889,5953],{"className":5885},[649],[572,5887],{"className":5888},[2282,4733],[572,5890,5892],{"className":5891},[4486],[572,5893,5895,5944],{"className":5894},[657,715],[572,5896,5898,5941],{"className":5897},[661],[572,5899,5902,5917,5925],{"className":5900,"style":5901},[665],"height:1.01em;",[572,5903,5904,5907],{"style":4749},[572,5905],{"className":5906,"style":674},[673],[572,5908,5910],{"className":5909},[733,734,735,736],[572,5911,5913],{"className":5912},[649,736],[572,5914,5916],{"className":5915},[649,736],"3\u002F2",[572,5918,5919,5922],{"style":4764},[572,5920],{"className":5921,"style":674},[673],[572,5923],{"className":5924,"style":4772},[4771],[572,5926,5928,5931],{"style":5927},"top:-3.485em;",[572,5929],{"className":5930,"style":674},[673],[572,5932,5934],{"className":5933},[733,734,735,736],[572,5935,5937],{"className":5936},[649,736],[572,5938,5940],{"className":5939},[649,736],"1\u002F2",[572,5942,744],{"className":5943},[743],[572,5945,5947],{"className":5946},[661],[572,5948,5951],{"className":5949,"style":5950},[665],"height:0.52em;",[572,5952],{},[572,5954],{"className":5955},[2358,4733],[572,5957,5959,5994],{"className":5958},[649],[572,5960,5962],{"className":5961},[649,653],[572,5963,5965],{"className":5964},[657],[572,5966,5968],{"className":5967},[661],[572,5969,5971,5979],{"className":5970,"style":666},[665],[572,5972,5973,5976],{"style":669},[572,5974],{"className":5975,"style":674},[673],[572,5977,872],{"className":5978},[649,678],[572,5980,5981,5984],{"style":669},[572,5982],{"className":5983,"style":674},[673],[572,5985,5987],{"className":5986,"style":689},[688],[572,5988,5990],{"className":5989,"style":694},[693],[696,5991,5992],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,5993],{"d":707},[572,5995,5997],{"className":5996},[711],[572,5998,6000,6020],{"className":5999},[657,715],[572,6001,6003,6017],{"className":6002},[661],[572,6004,6006],{"className":6005,"style":722},[665],[572,6007,6008,6011],{"style":957},[572,6009],{"className":6010,"style":729},[673],[572,6012,6014],{"className":6013},[733,734,735,736],[572,6015,1529],{"className":6016},[649,736],[572,6018,744],{"className":6019},[743],[572,6021,6023],{"className":6022},[661],[572,6024,6026],{"className":6025,"style":751},[665],[572,6027],{},[572,6029],{"className":6030,"style":1421},[761],[572,6032,1322],{"className":6033},[1425],[572,6035],{"className":6036,"style":1421},[761],[572,6038,6040,6043,6115,6118,6121],{"className":6039},[640],[572,6041],{"className":6042,"style":1345},[644],[572,6044,6046,6081],{"className":6045},[649],[572,6047,6049],{"className":6048},[649,653],[572,6050,6052],{"className":6051},[657],[572,6053,6055],{"className":6054},[661],[572,6056,6058,6066],{"className":6057,"style":666},[665],[572,6059,6060,6063],{"style":669},[572,6061],{"className":6062,"style":674},[673],[572,6064,600],{"className":6065,"style":679},[649,678],[572,6067,6068,6071],{"style":669},[572,6069],{"className":6070,"style":674},[673],[572,6072,6074],{"className":6073,"style":689},[688],[572,6075,6077],{"className":6076,"style":694},[693],[696,6078,6079],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,6080],{"d":707},[572,6082,6084],{"className":6083},[711],[572,6085,6087,6107],{"className":6086},[657,715],[572,6088,6090,6104],{"className":6089},[661],[572,6091,6093],{"className":6092,"style":722},[665],[572,6094,6095,6098],{"style":725},[572,6096],{"className":6097,"style":729},[673],[572,6099,6101],{"className":6100},[733,734,735,736],[572,6102,3890],{"className":6103},[649,736],[572,6105,744],{"className":6106},[743],[572,6108,6110],{"className":6109},[661],[572,6111,6113],{"className":6112,"style":751},[665],[572,6114],{},[572,6116],{"className":6117,"style":4713},[761],[572,6119,1858],{"className":6120},[2031],[572,6122],{"className":6123,"style":4713},[761],[572,6125,6127,6130,6198,6270,6273,6276],{"className":6126},[640],[572,6128],{"className":6129,"style":4726},[644],[572,6131,6133,6136,6195],{"className":6132},[649],[572,6134],{"className":6135},[2282,4733],[572,6137,6139],{"className":6138},[4486],[572,6140,6142,6187],{"className":6141},[657,715],[572,6143,6145,6184],{"className":6144},[661],[572,6146,6148,6162,6170],{"className":6147,"style":4746},[665],[572,6149,6150,6153],{"style":4749},[572,6151],{"className":6152,"style":674},[673],[572,6154,6156],{"className":6155},[733,734,735,736],[572,6157,6159],{"className":6158},[649,736],[572,6160,1529],{"className":6161},[649,736],[572,6163,6164,6167],{"style":4764},[572,6165],{"className":6166,"style":674},[673],[572,6168],{"className":6169,"style":4772},[4771],[572,6171,6172,6175],{"style":4775},[572,6173],{"className":6174,"style":674},[673],[572,6176,6178],{"className":6177},[733,734,735,736],[572,6179,6181],{"className":6180},[649,736],[572,6182,608],{"className":6183},[649,736],[572,6185,744],{"className":6186},[743],[572,6188,6190],{"className":6189},[661],[572,6191,6193],{"className":6192,"style":4797},[665],[572,6194],{},[572,6196],{"className":6197},[2358,4733],[572,6199,6201,6236],{"className":6200},[649],[572,6202,6204],{"className":6203},[649,653],[572,6205,6207],{"className":6206},[657],[572,6208,6210],{"className":6209},[661],[572,6211,6213,6221],{"className":6212,"style":666},[665],[572,6214,6215,6218],{"style":669},[572,6216],{"className":6217,"style":674},[673],[572,6219,872],{"className":6220},[649,678],[572,6222,6223,6226],{"style":669},[572,6224],{"className":6225,"style":674},[673],[572,6227,6229],{"className":6228,"style":689},[688],[572,6230,6232],{"className":6231,"style":694},[693],[696,6233,6234],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,6235],{"d":707},[572,6237,6239],{"className":6238},[711],[572,6240,6242,6262],{"className":6241},[657,715],[572,6243,6245,6259],{"className":6244},[661],[572,6246,6248],{"className":6247,"style":722},[665],[572,6249,6250,6253],{"style":957},[572,6251],{"className":6252,"style":729},[673],[572,6254,6256],{"className":6255},[733,734,735,736],[572,6257,608],{"className":6258},[649,736],[572,6260,744],{"className":6261},[743],[572,6263,6265],{"className":6264},[661],[572,6266,6268],{"className":6267,"style":751},[665],[572,6269],{},[572,6271],{"className":6272,"style":4713},[761],[572,6274,1858],{"className":6275},[2031],[572,6277],{"className":6278,"style":4713},[761],[572,6280,6282,6285,6353,6425,6428,6431],{"className":6281},[640],[572,6283],{"className":6284,"style":4726},[644],[572,6286,6288,6291,6350],{"className":6287},[649],[572,6289],{"className":6290},[2282,4733],[572,6292,6294],{"className":6293},[4486],[572,6295,6297,6342],{"className":6296},[657,715],[572,6298,6300,6339],{"className":6299},[661],[572,6301,6303,6317,6325],{"className":6302,"style":4746},[665],[572,6304,6305,6308],{"style":4749},[572,6306],{"className":6307,"style":674},[673],[572,6309,6311],{"className":6310},[733,734,735,736],[572,6312,6314],{"className":6313},[649,736],[572,6315,3890],{"className":6316},[649,736],[572,6318,6319,6322],{"style":4764},[572,6320],{"className":6321,"style":674},[673],[572,6323],{"className":6324,"style":4772},[4771],[572,6326,6327,6330],{"style":4775},[572,6328],{"className":6329,"style":674},[673],[572,6331,6333],{"className":6332},[733,734,735,736],[572,6334,6336],{"className":6335},[649,736],[572,6337,608],{"className":6338},[649,736],[572,6340,744],{"className":6341},[743],[572,6343,6345],{"className":6344},[661],[572,6346,6348],{"className":6347,"style":4797},[665],[572,6349],{},[572,6351],{"className":6352},[2358,4733],[572,6354,6356,6391],{"className":6355},[649],[572,6357,6359],{"className":6358},[649,653],[572,6360,6362],{"className":6361},[657],[572,6363,6365],{"className":6364},[661],[572,6366,6368,6376],{"className":6367,"style":666},[665],[572,6369,6370,6373],{"style":669},[572,6371],{"className":6372,"style":674},[673],[572,6374,872],{"className":6375},[649,678],[572,6377,6378,6381],{"style":669},[572,6379],{"className":6380,"style":674},[673],[572,6382,6384],{"className":6383,"style":689},[688],[572,6385,6387],{"className":6386,"style":694},[693],[696,6388,6389],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,6390],{"d":707},[572,6392,6394],{"className":6393},[711],[572,6395,6397,6417],{"className":6396},[657,715],[572,6398,6400,6414],{"className":6399},[661],[572,6401,6403],{"className":6402,"style":722},[665],[572,6404,6405,6408],{"style":957},[572,6406],{"className":6407,"style":729},[673],[572,6409,6411],{"className":6410},[733,734,735,736],[572,6412,1529],{"className":6413},[649,736],[572,6415,744],{"className":6416},[743],[572,6418,6420],{"className":6419},[661],[572,6421,6423],{"className":6422,"style":751},[665],[572,6424],{},[572,6426],{"className":6427,"style":1421},[761],[572,6429,1322],{"className":6430},[1425],[572,6432],{"className":6433,"style":1421},[761],[572,6435,6437,6440],{"className":6436},[640],[572,6438],{"className":6439,"style":4890},[644],[572,6441,6443,6449,6452,6520,6523,6526,6529,6597,6600,6603,6606,6674],{"className":6442},[766],[572,6444,6446],{"className":6445,"style":4898},[2282,4897],[572,6447,3335],{"className":6448},[4902,4903],[572,6450,1858],{"className":6451},[649],[572,6453,6455,6458,6517],{"className":6454},[649],[572,6456],{"className":6457},[2282,4733],[572,6459,6461],{"className":6460},[4486],[572,6462,6464,6509],{"className":6463},[657,715],[572,6465,6467,6506],{"className":6466},[661],[572,6468,6470,6484,6492],{"className":6469,"style":4746},[665],[572,6471,6472,6475],{"style":4749},[572,6473],{"className":6474,"style":674},[673],[572,6476,6478],{"className":6477},[733,734,735,736],[572,6479,6481],{"className":6480},[649,736],[572,6482,3890],{"className":6483},[649,736],[572,6485,6486,6489],{"style":4764},[572,6487],{"className":6488,"style":674},[673],[572,6490],{"className":6491,"style":4772},[4771],[572,6493,6494,6497],{"style":4775},[572,6495],{"className":6496,"style":674},[673],[572,6498,6500],{"className":6499},[733,734,735,736],[572,6501,6503],{"className":6502},[649,736],[572,6504,1529],{"className":6505},[649,736],[572,6507,744],{"className":6508},[743],[572,6510,6512],{"className":6511},[661],[572,6513,6515],{"className":6514,"style":4797},[665],[572,6516],{},[572,6518],{"className":6519},[2358,4733],[572,6521,611],{"className":6522},[757],[572,6524,3550],{"className":6525},[761],[572,6527],{"className":6528,"style":762},[761],[572,6530,6532,6535,6594],{"className":6531},[649],[572,6533],{"className":6534},[2282,4733],[572,6536,6538],{"className":6537},[4486],[572,6539,6541,6586],{"className":6540},[657,715],[572,6542,6544,6583],{"className":6543},[661],[572,6545,6547,6561,6569],{"className":6546,"style":4746},[665],[572,6548,6549,6552],{"style":4749},[572,6550],{"className":6551,"style":674},[673],[572,6553,6555],{"className":6554},[733,734,735,736],[572,6556,6558],{"className":6557},[649,736],[572,6559,3890],{"className":6560},[649,736],[572,6562,6563,6566],{"style":4764},[572,6564],{"className":6565,"style":674},[673],[572,6567],{"className":6568,"style":4772},[4771],[572,6570,6571,6574],{"style":4775},[572,6572],{"className":6573,"style":674},[673],[572,6575,6577],{"className":6576},[733,734,735,736],[572,6578,6580],{"className":6579},[649,736],[572,6581,1529],{"className":6582},[649,736],[572,6584,744],{"className":6585},[743],[572,6587,6589],{"className":6588},[661],[572,6590,6592],{"className":6591,"style":4797},[665],[572,6593],{},[572,6595],{"className":6596},[2358,4733],[572,6598,611],{"className":6599},[757],[572,6601,3550],{"className":6602},[761],[572,6604],{"className":6605,"style":762},[761],[572,6607,6609,6612,6671],{"className":6608},[649],[572,6610],{"className":6611},[2282,4733],[572,6613,6615],{"className":6614},[4486],[572,6616,6618,6663],{"className":6617},[657,715],[572,6619,6621,6660],{"className":6620},[661],[572,6622,6624,6638,6646],{"className":6623,"style":4746},[665],[572,6625,6626,6629],{"style":4749},[572,6627],{"className":6628,"style":674},[673],[572,6630,6632],{"className":6631},[733,734,735,736],[572,6633,6635],{"className":6634},[649,736],[572,6636,3890],{"className":6637},[649,736],[572,6639,6640,6643],{"style":4764},[572,6641],{"className":6642,"style":674},[673],[572,6644],{"className":6645,"style":4772},[4771],[572,6647,6648,6651],{"style":4775},[572,6649],{"className":6650,"style":674},[673],[572,6652,6654],{"className":6653},[733,734,735,736],[572,6655,6657],{"className":6656},[649,736],[572,6658,1529],{"className":6659},[649,736],[572,6661,744],{"className":6662},[743],[572,6664,6666],{"className":6665},[661],[572,6667,6669],{"className":6668,"style":4797},[665],[572,6670],{},[572,6672],{"className":6673},[2358,4733],[572,6675,6677],{"className":6676,"style":4898},[2358,4897],[572,6678,3341],{"className":6679},[4902,4903],[564,6681,6682,6683,6890,6891,6975,6976,7004,7005,7085,7086,7166],{},"Alle drei Skalarprodukte ",[572,6684,6686,6724],{"className":6685},[575],[572,6687,6689],{"className":6688},[579],[581,6690,6691],{"xmlns":583},[585,6692,6693,6721],{},[588,6694,6695,6697,6707,6709,6719],{},[602,6696,3303],{"stretchy":2090},[591,6698,6699,6705],{},[594,6700,6701,6703],{"accent":596},[598,6702,872],{},[602,6704,604],{},[598,6706,1726],{},[602,6708,611],{"separator":596},[591,6710,6711,6717],{},[594,6712,6713,6715],{"accent":596},[598,6714,872],{},[602,6716,604],{},[598,6718,1524],{},[602,6720,3314],{"stretchy":2090},[629,6722,6723],{"encoding":631},"\\langle \\vec u_j, \\vec u_k \\rangle",[572,6725,6727],{"className":6726,"ariaHidden":596},[636],[572,6728,6730,6734,6737,6809,6812,6815,6887],{"className":6729},[640],[572,6731],{"className":6732,"style":6733},[644],"height:1.0361em;vertical-align:-0.2861em;",[572,6735,3303],{"className":6736},[2282],[572,6738,6740,6775],{"className":6739},[649],[572,6741,6743],{"className":6742},[649,653],[572,6744,6746],{"className":6745},[657],[572,6747,6749],{"className":6748},[661],[572,6750,6752,6760],{"className":6751,"style":666},[665],[572,6753,6754,6757],{"style":669},[572,6755],{"className":6756,"style":674},[673],[572,6758,872],{"className":6759},[649,678],[572,6761,6762,6765],{"style":669},[572,6763],{"className":6764,"style":674},[673],[572,6766,6768],{"className":6767,"style":689},[688],[572,6769,6771],{"className":6770,"style":694},[693],[696,6772,6773],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,6774],{"d":707},[572,6776,6778],{"className":6777},[711],[572,6779,6781,6801],{"className":6780},[657,715],[572,6782,6784,6798],{"className":6783},[661],[572,6785,6787],{"className":6786,"style":1790},[665],[572,6788,6789,6792],{"style":957},[572,6790],{"className":6791,"style":729},[673],[572,6793,6795],{"className":6794},[733,734,735,736],[572,6796,1726],{"className":6797,"style":1802},[649,678,736],[572,6799,744],{"className":6800},[743],[572,6802,6804],{"className":6803},[661],[572,6805,6807],{"className":6806,"style":1812},[665],[572,6808],{},[572,6810,611],{"className":6811},[757],[572,6813],{"className":6814,"style":762},[761],[572,6816,6818,6853],{"className":6817},[649],[572,6819,6821],{"className":6820},[649,653],[572,6822,6824],{"className":6823},[657],[572,6825,6827],{"className":6826},[661],[572,6828,6830,6838],{"className":6829,"style":666},[665],[572,6831,6832,6835],{"style":669},[572,6833],{"className":6834,"style":674},[673],[572,6836,872],{"className":6837},[649,678],[572,6839,6840,6843],{"style":669},[572,6841],{"className":6842,"style":674},[673],[572,6844,6846],{"className":6845,"style":689},[688],[572,6847,6849],{"className":6848,"style":694},[693],[696,6850,6851],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,6852],{"d":707},[572,6854,6856],{"className":6855},[711],[572,6857,6859,6879],{"className":6858},[657,715],[572,6860,6862,6876],{"className":6861},[661],[572,6863,6865],{"className":6864,"style":1680},[665],[572,6866,6867,6870],{"style":957},[572,6868],{"className":6869,"style":729},[673],[572,6871,6873],{"className":6872},[733,734,735,736],[572,6874,1524],{"className":6875,"style":1554},[649,678,736],[572,6877,744],{"className":6878},[743],[572,6880,6882],{"className":6881},[661],[572,6883,6885],{"className":6884,"style":751},[665],[572,6886],{},[572,6888,3314],{"className":6889},[2358]," mit ",[572,6892,6894,6912],{"className":6893},[575],[572,6895,6897],{"className":6896},[579],[581,6898,6899],{"xmlns":583},[585,6900,6901,6909],{},[588,6902,6903,6905,6907],{},[598,6904,1726],{},[602,6906,3216],{"mathvariant":2086},[598,6908,1524],{},[629,6910,6911],{"encoding":631},"j \\neq k",[572,6913,6915,6966],{"className":6914,"ariaHidden":596},[636],[572,6916,6918,6921,6924,6927,6963],{"className":6917},[640],[572,6919],{"className":6920,"style":3231},[644],[572,6922,1726],{"className":6923,"style":1802},[649,678],[572,6925],{"className":6926,"style":1421},[761],[572,6928,6930,6957,6960],{"className":6929},[1425],[572,6931,6933],{"className":6932},[1425],[572,6934,6936],{"className":6935},[649,3241],[572,6937,6939],{"className":6938},[3245],[572,6940,6942,6945,6954],{"className":6941},[3249],[572,6943],{"className":6944,"style":3231},[644],[572,6946,6948],{"className":6947},[3256],[572,6949,6951],{"className":6950},[649],[572,6952,3263],{"className":6953},[1425],[572,6955],{"className":6956},[3267],[572,6958],{"className":6959},[761,3271],[572,6961,1322],{"className":6962},[1425],[572,6964],{"className":6965,"style":1421},[761],[572,6967,6969,6972],{"className":6968},[640],[572,6970],{"className":6971,"style":1550},[644],[572,6973,1524],{"className":6974,"style":1554},[649,678]," sind ",[572,6977,6979,6992],{"className":6978},[575],[572,6980,6982],{"className":6981},[579],[581,6983,6984],{"xmlns":583},[585,6985,6986,6990],{},[588,6987,6988],{},[606,6989,2951],{},[629,6991,2951],{"encoding":631},[572,6993,6995],{"className":6994,"ariaHidden":596},[636],[572,6996,6998,7001],{"className":6997},[640],[572,6999],{"className":7000,"style":3284},[644],[572,7002,2951],{"className":7003},[649],". Normiert (mit den Vielfachen ",[572,7006,7008,7040],{"className":7007},[575],[572,7009,7011],{"className":7010},[579],[581,7012,7013],{"xmlns":583},[585,7014,7015,7037],{},[588,7016,7017,7019,7021,7023,7025,7027,7029,7031,7033,7035],{},[602,7018,3335],{"stretchy":2090},[606,7020,608],{},[602,7022,611],{"separator":596},[3351,7024,3550],{},[602,7026,1858],{},[606,7028,608],{},[602,7030,611],{"separator":596},[3351,7032,3550],{},[606,7034,1529],{},[602,7036,3341],{"stretchy":2090},[629,7038,7039],{"encoding":631},"(1,\\ -1,\\ 2)",[572,7041,7043],{"className":7042,"ariaHidden":596},[636],[572,7044,7046,7049,7052,7055,7058,7061,7064,7067,7070,7073,7076,7079,7082],{"className":7045},[640],[572,7047],{"className":7048,"style":2203},[644],[572,7050,3335],{"className":7051},[2282],[572,7053,608],{"className":7054},[649],[572,7056,611],{"className":7057},[757],[572,7059,3550],{"className":7060},[761],[572,7062],{"className":7063,"style":762},[761],[572,7065,1858],{"className":7066},[649],[572,7068,608],{"className":7069},[649],[572,7071,611],{"className":7072},[757],[572,7074,3550],{"className":7075},[761],[572,7077],{"className":7078,"style":762},[761],[572,7080,1529],{"className":7081},[649],[572,7083,3341],{"className":7084},[2358]," und ",[572,7087,7089,7121],{"className":7088},[575],[572,7090,7092],{"className":7091},[579],[581,7093,7094],{"xmlns":583},[585,7095,7096,7118],{},[588,7097,7098,7100,7102,7104,7106,7108,7110,7112,7114,7116],{},[602,7099,3335],{"stretchy":2090},[602,7101,1858],{},[606,7103,608],{},[602,7105,611],{"separator":596},[3351,7107,3550],{},[606,7109,608],{},[602,7111,611],{"separator":596},[3351,7113,3550],{},[606,7115,608],{},[602,7117,3341],{"stretchy":2090},[629,7119,7120],{"encoding":631},"(-1,\\ 1,\\ 1)",[572,7122,7124],{"className":7123,"ariaHidden":596},[636],[572,7125,7127,7130,7133,7136,7139,7142,7145,7148,7151,7154,7157,7160,7163],{"className":7126},[640],[572,7128],{"className":7129,"style":2203},[644],[572,7131,3335],{"className":7132},[2282],[572,7134,1858],{"className":7135},[649],[572,7137,608],{"className":7138},[649],[572,7140,611],{"className":7141},[757],[572,7143,3550],{"className":7144},[761],[572,7146],{"className":7147,"style":762},[761],[572,7149,608],{"className":7150},[649],[572,7152,611],{"className":7153},[757],[572,7155,3550],{"className":7156},[761],[572,7158],{"className":7159,"style":762},[761],[572,7161,608],{"className":7162},[649],[572,7164,3341],{"className":7165},[2358]," gerechnet):",[572,7168,7171],{"className":7169},[7170],"katex-display",[572,7172,7174,7324],{"className":7173},[575],[572,7175,7177],{"className":7176},[579],[581,7178,7180],{"xmlns":583,"display":7179},"block",[585,7181,7182,7321],{},[588,7183,7184,7194,7196,7207,7209,7211,7213,7215,7217,7219,7221,7223,7225,7227,7230,7240,7242,7253,7255,7257,7259,7261,7263,7265,7267,7269,7271,7273,7275,7277,7287,7289,7299,7301,7303,7305,7307,7309,7311,7313,7315,7317,7319],{},[591,7185,7186,7192],{},[594,7187,7188,7190],{"accent":596},[598,7189,1090],{},[602,7191,604],{},[606,7193,608],{},[602,7195,1322],{},[4509,7197,7198],{"scriptlevel":2951,"displaystyle":2090},[4486,7199,7200,7202],{},[606,7201,608],{},[7203,7204,7205],"msqrt",{},[606,7206,1529],{},[602,7208,3335],{"stretchy":2090},[606,7210,608],{},[602,7212,611],{"separator":596},[3351,7214,3550],{},[606,7216,608],{},[602,7218,611],{"separator":596},[3351,7220,3550],{},[606,7222,2951],{},[602,7224,3341],{"stretchy":2090},[602,7226,611],{"separator":596},[761,7228],{"width":7229},"1em",[591,7231,7232,7238],{},[594,7233,7234,7236],{"accent":596},[598,7235,1090],{},[602,7237,604],{},[606,7239,1529],{},[602,7241,1322],{},[4509,7243,7244],{"scriptlevel":2951,"displaystyle":2090},[4486,7245,7246,7248],{},[606,7247,608],{},[7203,7249,7250],{},[606,7251,7252],{},"6",[602,7254,3335],{"stretchy":2090},[606,7256,608],{},[602,7258,611],{"separator":596},[3351,7260,3550],{},[602,7262,1858],{},[606,7264,608],{},[602,7266,611],{"separator":596},[3351,7268,3550],{},[606,7270,1529],{},[602,7272,3341],{"stretchy":2090},[602,7274,611],{"separator":596},[761,7276],{"width":7229},[591,7278,7279,7285],{},[594,7280,7281,7283],{"accent":596},[598,7282,1090],{},[602,7284,604],{},[606,7286,3890],{},[602,7288,1322],{},[4509,7290,7291],{"scriptlevel":2951,"displaystyle":2090},[4486,7292,7293,7295],{},[606,7294,608],{},[7203,7296,7297],{},[606,7298,3890],{},[602,7300,3335],{"stretchy":2090},[602,7302,1858],{},[606,7304,608],{},[602,7306,611],{"separator":596},[3351,7308,3550],{},[606,7310,608],{},[602,7312,611],{"separator":596},[3351,7314,3550],{},[606,7316,608],{},[602,7318,3341],{"stretchy":2090},[598,7320,1288],{"mathvariant":2086},[629,7322,7323],{"encoding":631},"\\vec w_1 = \\tfrac{1}{\\sqrt2}(1,\\ 1,\\ 0), \\quad \\vec w_2 = \\tfrac{1}{\\sqrt6}(1,\\ -1,\\ 2), \\quad \\vec w_3 = \\tfrac{1}{\\sqrt3}(-1,\\ 1,\\ 1).",[572,7325,7327,7414,7669,7910],{"className":7326,"ariaHidden":596},[636],[572,7328,7330,7333,7405,7408,7411],{"className":7329},[640],[572,7331],{"className":7332,"style":1345},[644],[572,7334,7336,7371],{"className":7335},[649],[572,7337,7339],{"className":7338},[649,653],[572,7340,7342],{"className":7341},[657],[572,7343,7345],{"className":7344},[661],[572,7346,7348,7356],{"className":7347,"style":666},[665],[572,7349,7350,7353],{"style":669},[572,7351],{"className":7352,"style":674},[673],[572,7354,1090],{"className":7355,"style":1146},[649,678],[572,7357,7358,7361],{"style":669},[572,7359],{"className":7360,"style":674},[673],[572,7362,7364],{"className":7363,"style":1155},[688],[572,7365,7367],{"className":7366,"style":694},[693],[696,7368,7369],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,7370],{"d":707},[572,7372,7374],{"className":7373},[711],[572,7375,7377,7397],{"className":7376},[657,715],[572,7378,7380,7394],{"className":7379},[661],[572,7381,7383],{"className":7382,"style":722},[665],[572,7384,7385,7388],{"style":1177},[572,7386],{"className":7387,"style":729},[673],[572,7389,7391],{"className":7390},[733,734,735,736],[572,7392,608],{"className":7393},[649,736],[572,7395,744],{"className":7396},[743],[572,7398,7400],{"className":7399},[661],[572,7401,7403],{"className":7402,"style":751},[665],[572,7404],{},[572,7406],{"className":7407,"style":1421},[761],[572,7409,1322],{"className":7410},[1425],[572,7412],{"className":7413,"style":1421},[761],[572,7415,7417,7421,7545,7548,7551,7554,7557,7560,7563,7566,7569,7572,7575,7578,7581,7585,7588,7660,7663,7666],{"className":7416},[640],[572,7418],{"className":7419,"style":7420},[644],"height:1.3831em;vertical-align:-0.538em;",[572,7422,7424,7427,7542],{"className":7423},[649],[572,7425],{"className":7426},[2282,4733],[572,7428,7430],{"className":7429},[4486],[572,7431,7433,7533],{"className":7432},[657,715],[572,7434,7436,7530],{"className":7435},[661],[572,7437,7439,7508,7516],{"className":7438,"style":4746},[665],[572,7440,7442,7445],{"style":7441},"top:-2.551em;",[572,7443],{"className":7444,"style":674},[673],[572,7446,7448],{"className":7447},[733,734,735,736],[572,7449,7451],{"className":7450},[649,736],[572,7452,7455],{"className":7453},[649,7454,736],"sqrt",[572,7456,7458,7499],{"className":7457},[657,715],[572,7459,7461,7496],{"className":7460},[661],[572,7462,7465,7476],{"className":7463,"style":7464},[665],"height:0.9128em;",[572,7466,7469,7472],{"className":7467,"style":669},[7468],"svg-align",[572,7470],{"className":7471,"style":674},[673],[572,7473,1529],{"className":7474,"style":7475},[649,736],"padding-left:0.833em;",[572,7477,7479,7482],{"style":7478},"top:-2.8728em;",[572,7480],{"className":7481,"style":674},[673],[572,7483,7487],{"className":7484,"style":7486},[7485,736],"hide-tail","min-width:0.853em;height:1.08em;",[696,7488,7493],{"xmlns":698,"width":7489,"height":7490,"viewBox":7491,"preserveAspectRatio":7492},"400em","1.08em","0 0 400000 1080","xMinYMin slice",[705,7494],{"d":7495},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[572,7497,744],{"className":7498},[743],[572,7500,7502],{"className":7501},[661],[572,7503,7506],{"className":7504,"style":7505},[665],"height:0.1272em;",[572,7507],{},[572,7509,7510,7513],{"style":4764},[572,7511],{"className":7512,"style":674},[673],[572,7514],{"className":7515,"style":4772},[4771],[572,7517,7518,7521],{"style":4775},[572,7519],{"className":7520,"style":674},[673],[572,7522,7524],{"className":7523},[733,734,735,736],[572,7525,7527],{"className":7526},[649,736],[572,7528,608],{"className":7529},[649,736],[572,7531,744],{"className":7532},[743],[572,7534,7536],{"className":7535},[661],[572,7537,7540],{"className":7538,"style":7539},[665],"height:0.538em;",[572,7541],{},[572,7543],{"className":7544},[2358,4733],[572,7546,3335],{"className":7547},[2282],[572,7549,608],{"className":7550},[649],[572,7552,611],{"className":7553},[757],[572,7555,3550],{"className":7556},[761],[572,7558],{"className":7559,"style":762},[761],[572,7561,608],{"className":7562},[649],[572,7564,611],{"className":7565},[757],[572,7567,3550],{"className":7568},[761],[572,7570],{"className":7571,"style":762},[761],[572,7573,2951],{"className":7574},[649],[572,7576,3341],{"className":7577},[2358],[572,7579,611],{"className":7580},[757],[572,7582],{"className":7583,"style":7584},[761],"margin-right:1em;",[572,7586],{"className":7587,"style":762},[761],[572,7589,7591,7626],{"className":7590},[649],[572,7592,7594],{"className":7593},[649,653],[572,7595,7597],{"className":7596},[657],[572,7598,7600],{"className":7599},[661],[572,7601,7603,7611],{"className":7602,"style":666},[665],[572,7604,7605,7608],{"style":669},[572,7606],{"className":7607,"style":674},[673],[572,7609,1090],{"className":7610,"style":1146},[649,678],[572,7612,7613,7616],{"style":669},[572,7614],{"className":7615,"style":674},[673],[572,7617,7619],{"className":7618,"style":1155},[688],[572,7620,7622],{"className":7621,"style":694},[693],[696,7623,7624],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,7625],{"d":707},[572,7627,7629],{"className":7628},[711],[572,7630,7632,7652],{"className":7631},[657,715],[572,7633,7635,7649],{"className":7634},[661],[572,7636,7638],{"className":7637,"style":722},[665],[572,7639,7640,7643],{"style":1177},[572,7641],{"className":7642,"style":729},[673],[572,7644,7646],{"className":7645},[733,734,735,736],[572,7647,1529],{"className":7648},[649,736],[572,7650,744],{"className":7651},[743],[572,7653,7655],{"className":7654},[661],[572,7656,7658],{"className":7657,"style":751},[665],[572,7659],{},[572,7661],{"className":7662,"style":1421},[761],[572,7664,1322],{"className":7665},[1425],[572,7667],{"className":7668,"style":1421},[761],[572,7670,7672,7675,7784,7787,7790,7793,7796,7799,7802,7805,7808,7811,7814,7817,7820,7823,7826,7829,7901,7904,7907],{"className":7671},[640],[572,7673],{"className":7674,"style":7420},[644],[572,7676,7678,7681,7781],{"className":7677},[649],[572,7679],{"className":7680},[2282,4733],[572,7682,7684],{"className":7683},[4486],[572,7685,7687,7773],{"className":7686},[657,715],[572,7688,7690,7770],{"className":7689},[661],[572,7691,7693,7748,7756],{"className":7692,"style":4746},[665],[572,7694,7695,7698],{"style":7441},[572,7696],{"className":7697,"style":674},[673],[572,7699,7701],{"className":7700},[733,734,735,736],[572,7702,7704],{"className":7703},[649,736],[572,7705,7707],{"className":7706},[649,7454,736],[572,7708,7710,7740],{"className":7709},[657,715],[572,7711,7713,7737],{"className":7712},[661],[572,7714,7716,7725],{"className":7715,"style":7464},[665],[572,7717,7719,7722],{"className":7718,"style":669},[7468],[572,7720],{"className":7721,"style":674},[673],[572,7723,7252],{"className":7724,"style":7475},[649,736],[572,7726,7727,7730],{"style":7478},[572,7728],{"className":7729,"style":674},[673],[572,7731,7733],{"className":7732,"style":7486},[7485,736],[696,7734,7735],{"xmlns":698,"width":7489,"height":7490,"viewBox":7491,"preserveAspectRatio":7492},[705,7736],{"d":7495},[572,7738,744],{"className":7739},[743],[572,7741,7743],{"className":7742},[661],[572,7744,7746],{"className":7745,"style":7505},[665],[572,7747],{},[572,7749,7750,7753],{"style":4764},[572,7751],{"className":7752,"style":674},[673],[572,7754],{"className":7755,"style":4772},[4771],[572,7757,7758,7761],{"style":4775},[572,7759],{"className":7760,"style":674},[673],[572,7762,7764],{"className":7763},[733,734,735,736],[572,7765,7767],{"className":7766},[649,736],[572,7768,608],{"className":7769},[649,736],[572,7771,744],{"className":7772},[743],[572,7774,7776],{"className":7775},[661],[572,7777,7779],{"className":7778,"style":7539},[665],[572,7780],{},[572,7782],{"className":7783},[2358,4733],[572,7785,3335],{"className":7786},[2282],[572,7788,608],{"className":7789},[649],[572,7791,611],{"className":7792},[757],[572,7794,3550],{"className":7795},[761],[572,7797],{"className":7798,"style":762},[761],[572,7800,1858],{"className":7801},[649],[572,7803,608],{"className":7804},[649],[572,7806,611],{"className":7807},[757],[572,7809,3550],{"className":7810},[761],[572,7812],{"className":7813,"style":762},[761],[572,7815,1529],{"className":7816},[649],[572,7818,3341],{"className":7819},[2358],[572,7821,611],{"className":7822},[757],[572,7824],{"className":7825,"style":7584},[761],[572,7827],{"className":7828,"style":762},[761],[572,7830,7832,7867],{"className":7831},[649],[572,7833,7835],{"className":7834},[649,653],[572,7836,7838],{"className":7837},[657],[572,7839,7841],{"className":7840},[661],[572,7842,7844,7852],{"className":7843,"style":666},[665],[572,7845,7846,7849],{"style":669},[572,7847],{"className":7848,"style":674},[673],[572,7850,1090],{"className":7851,"style":1146},[649,678],[572,7853,7854,7857],{"style":669},[572,7855],{"className":7856,"style":674},[673],[572,7858,7860],{"className":7859,"style":1155},[688],[572,7861,7863],{"className":7862,"style":694},[693],[696,7864,7865],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,7866],{"d":707},[572,7868,7870],{"className":7869},[711],[572,7871,7873,7893],{"className":7872},[657,715],[572,7874,7876,7890],{"className":7875},[661],[572,7877,7879],{"className":7878,"style":722},[665],[572,7880,7881,7884],{"style":1177},[572,7882],{"className":7883,"style":729},[673],[572,7885,7887],{"className":7886},[733,734,735,736],[572,7888,3890],{"className":7889},[649,736],[572,7891,744],{"className":7892},[743],[572,7894,7896],{"className":7895},[661],[572,7897,7899],{"className":7898,"style":751},[665],[572,7900],{},[572,7902],{"className":7903,"style":1421},[761],[572,7905,1322],{"className":7906},[1425],[572,7908],{"className":7909,"style":1421},[761],[572,7911,7913,7916,8025,8028,8031,8034,8037,8040,8043,8046,8049,8052,8055,8058,8061],{"className":7912},[640],[572,7914],{"className":7915,"style":7420},[644],[572,7917,7919,7922,8022],{"className":7918},[649],[572,7920],{"className":7921},[2282,4733],[572,7923,7925],{"className":7924},[4486],[572,7926,7928,8014],{"className":7927},[657,715],[572,7929,7931,8011],{"className":7930},[661],[572,7932,7934,7989,7997],{"className":7933,"style":4746},[665],[572,7935,7936,7939],{"style":7441},[572,7937],{"className":7938,"style":674},[673],[572,7940,7942],{"className":7941},[733,734,735,736],[572,7943,7945],{"className":7944},[649,736],[572,7946,7948],{"className":7947},[649,7454,736],[572,7949,7951,7981],{"className":7950},[657,715],[572,7952,7954,7978],{"className":7953},[661],[572,7955,7957,7966],{"className":7956,"style":7464},[665],[572,7958,7960,7963],{"className":7959,"style":669},[7468],[572,7961],{"className":7962,"style":674},[673],[572,7964,3890],{"className":7965,"style":7475},[649,736],[572,7967,7968,7971],{"style":7478},[572,7969],{"className":7970,"style":674},[673],[572,7972,7974],{"className":7973,"style":7486},[7485,736],[696,7975,7976],{"xmlns":698,"width":7489,"height":7490,"viewBox":7491,"preserveAspectRatio":7492},[705,7977],{"d":7495},[572,7979,744],{"className":7980},[743],[572,7982,7984],{"className":7983},[661],[572,7985,7987],{"className":7986,"style":7505},[665],[572,7988],{},[572,7990,7991,7994],{"style":4764},[572,7992],{"className":7993,"style":674},[673],[572,7995],{"className":7996,"style":4772},[4771],[572,7998,7999,8002],{"style":4775},[572,8000],{"className":8001,"style":674},[673],[572,8003,8005],{"className":8004},[733,734,735,736],[572,8006,8008],{"className":8007},[649,736],[572,8009,608],{"className":8010},[649,736],[572,8012,744],{"className":8013},[743],[572,8015,8017],{"className":8016},[661],[572,8018,8020],{"className":8019,"style":7539},[665],[572,8021],{},[572,8023],{"className":8024},[2358,4733],[572,8026,3335],{"className":8027},[2282],[572,8029,1858],{"className":8030},[649],[572,8032,608],{"className":8033},[649],[572,8035,611],{"className":8036},[757],[572,8038,3550],{"className":8039},[761],[572,8041],{"className":8042,"style":762},[761],[572,8044,608],{"className":8045},[649],[572,8047,611],{"className":8048},[757],[572,8050,3550],{"className":8051},[761],[572,8053],{"className":8054,"style":762},[761],[572,8056,608],{"className":8057},[649],[572,8059,3341],{"className":8060},[2358],[572,8062,1288],{"className":8063},[649],[559,8065,8067],{"id":8066},"typische-fehler","Typische Fehler",[8069,8070,8071,8396,8813,9551],"ul",{},[1296,8072,8073,8074,8179,8180,853,8183,8289,8290,8395],{},"Von ",[572,8075,8077,8098],{"className":8076},[575],[572,8078,8080],{"className":8079},[579],[581,8081,8082],{"xmlns":583},[585,8083,8084,8096],{},[588,8085,8086],{},[591,8087,8088,8094],{},[594,8089,8090,8092],{"accent":596},[598,8091,600],{},[602,8093,604],{},[598,8095,1524],{},[629,8097,1620],{"encoding":631},[572,8099,8101],{"className":8100,"ariaHidden":596},[636],[572,8102,8104,8107],{"className":8103},[640],[572,8105],{"className":8106,"style":1345},[644],[572,8108,8110,8145],{"className":8109},[649],[572,8111,8113],{"className":8112},[649,653],[572,8114,8116],{"className":8115},[657],[572,8117,8119],{"className":8118},[661],[572,8120,8122,8130],{"className":8121,"style":666},[665],[572,8123,8124,8127],{"style":669},[572,8125],{"className":8126,"style":674},[673],[572,8128,600],{"className":8129,"style":679},[649,678],[572,8131,8132,8135],{"style":669},[572,8133],{"className":8134,"style":674},[673],[572,8136,8138],{"className":8137,"style":689},[688],[572,8139,8141],{"className":8140,"style":694},[693],[696,8142,8143],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8144],{"d":707},[572,8146,8148],{"className":8147},[711],[572,8149,8151,8171],{"className":8150},[657,715],[572,8152,8154,8168],{"className":8153},[661],[572,8155,8157],{"className":8156,"style":1680},[665],[572,8158,8159,8162],{"style":725},[572,8160],{"className":8161,"style":729},[673],[572,8163,8165],{"className":8164},[733,734,735,736],[572,8166,1524],{"className":8167,"style":1554},[649,678,736],[572,8169,744],{"className":8170},[743],[572,8172,8174],{"className":8173},[661],[572,8175,8177],{"className":8176,"style":751},[665],[572,8178],{}," die Projektionen auf die ",[568,8181,8182],{},"ursprünglichen",[572,8184,8186,8208],{"className":8185},[575],[572,8187,8189],{"className":8188},[579],[581,8190,8191],{"xmlns":583},[585,8192,8193,8205],{},[588,8194,8195],{},[591,8196,8197,8203],{},[594,8198,8199,8201],{"accent":596},[598,8200,600],{},[602,8202,604],{},[598,8204,1726],{},[629,8206,8207],{"encoding":631},"\\vec v_j",[572,8209,8211],{"className":8210,"ariaHidden":596},[636],[572,8212,8214,8217],{"className":8213},[640],[572,8215],{"className":8216,"style":1739},[644],[572,8218,8220,8255],{"className":8219},[649],[572,8221,8223],{"className":8222},[649,653],[572,8224,8226],{"className":8225},[657],[572,8227,8229],{"className":8228},[661],[572,8230,8232,8240],{"className":8231,"style":666},[665],[572,8233,8234,8237],{"style":669},[572,8235],{"className":8236,"style":674},[673],[572,8238,600],{"className":8239,"style":679},[649,678],[572,8241,8242,8245],{"style":669},[572,8243],{"className":8244,"style":674},[673],[572,8246,8248],{"className":8247,"style":689},[688],[572,8249,8251],{"className":8250,"style":694},[693],[696,8252,8253],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8254],{"d":707},[572,8256,8258],{"className":8257},[711],[572,8259,8261,8281],{"className":8260},[657,715],[572,8262,8264,8278],{"className":8263},[661],[572,8265,8267],{"className":8266,"style":1790},[665],[572,8268,8269,8272],{"style":725},[572,8270],{"className":8271,"style":729},[673],[572,8273,8275],{"className":8274},[733,734,735,736],[572,8276,1726],{"className":8277,"style":1802},[649,678,736],[572,8279,744],{"className":8280},[743],[572,8282,8284],{"className":8283},[661],[572,8285,8287],{"className":8286,"style":1812},[665],[572,8288],{}," statt auf die bereits orthogonalisierten ",[572,8291,8293,8314],{"className":8292},[575],[572,8294,8296],{"className":8295},[579],[581,8297,8298],{"xmlns":583},[585,8299,8300,8312],{},[588,8301,8302],{},[591,8303,8304,8310],{},[594,8305,8306,8308],{"accent":596},[598,8307,872],{},[602,8309,604],{},[598,8311,1726],{},[629,8313,1729],{"encoding":631},[572,8315,8317],{"className":8316,"ariaHidden":596},[636],[572,8318,8320,8323],{"className":8319},[640],[572,8321],{"className":8322,"style":1739},[644],[572,8324,8326,8361],{"className":8325},[649],[572,8327,8329],{"className":8328},[649,653],[572,8330,8332],{"className":8331},[657],[572,8333,8335],{"className":8334},[661],[572,8336,8338,8346],{"className":8337,"style":666},[665],[572,8339,8340,8343],{"style":669},[572,8341],{"className":8342,"style":674},[673],[572,8344,872],{"className":8345},[649,678],[572,8347,8348,8351],{"style":669},[572,8349],{"className":8350,"style":674},[673],[572,8352,8354],{"className":8353,"style":689},[688],[572,8355,8357],{"className":8356,"style":694},[693],[696,8358,8359],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8360],{"d":707},[572,8362,8364],{"className":8363},[711],[572,8365,8367,8387],{"className":8366},[657,715],[572,8368,8370,8384],{"className":8369},[661],[572,8371,8373],{"className":8372,"style":1790},[665],[572,8374,8375,8378],{"style":957},[572,8376],{"className":8377,"style":729},[673],[572,8379,8381],{"className":8380},[733,734,735,736],[572,8382,1726],{"className":8383,"style":1802},[649,678,736],[572,8385,744],{"className":8386},[743],[572,8388,8390],{"className":8389},[661],[572,8391,8393],{"className":8392,"style":1812},[665],[572,8394],{}," abziehen.",[1296,8397,8398,8399,8605,8606,8812],{},"Im Nenner ",[572,8400,8402,8440],{"className":8401},[575],[572,8403,8405],{"className":8404},[579],[581,8406,8407],{"xmlns":583},[585,8408,8409,8437],{},[588,8410,8411,8413,8423,8425,8435],{},[602,8412,3303],{"stretchy":2090},[591,8414,8415,8421],{},[594,8416,8417,8419],{"accent":596},[598,8418,600],{},[602,8420,604],{},[598,8422,1524],{},[602,8424,611],{"separator":596},[591,8426,8427,8433],{},[594,8428,8429,8431],{"accent":596},[598,8430,600],{},[602,8432,604],{},[598,8434,1524],{},[602,8436,3314],{"stretchy":2090},[629,8438,8439],{"encoding":631},"\\langle \\vec v_k, \\vec v_k \\rangle",[572,8441,8443],{"className":8442,"ariaHidden":596},[636],[572,8444,8446,8449,8452,8524,8527,8530,8602],{"className":8445},[640],[572,8447],{"className":8448,"style":2203},[644],[572,8450,3303],{"className":8451},[2282],[572,8453,8455,8490],{"className":8454},[649],[572,8456,8458],{"className":8457},[649,653],[572,8459,8461],{"className":8460},[657],[572,8462,8464],{"className":8463},[661],[572,8465,8467,8475],{"className":8466,"style":666},[665],[572,8468,8469,8472],{"style":669},[572,8470],{"className":8471,"style":674},[673],[572,8473,600],{"className":8474,"style":679},[649,678],[572,8476,8477,8480],{"style":669},[572,8478],{"className":8479,"style":674},[673],[572,8481,8483],{"className":8482,"style":689},[688],[572,8484,8486],{"className":8485,"style":694},[693],[696,8487,8488],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8489],{"d":707},[572,8491,8493],{"className":8492},[711],[572,8494,8496,8516],{"className":8495},[657,715],[572,8497,8499,8513],{"className":8498},[661],[572,8500,8502],{"className":8501,"style":1680},[665],[572,8503,8504,8507],{"style":725},[572,8505],{"className":8506,"style":729},[673],[572,8508,8510],{"className":8509},[733,734,735,736],[572,8511,1524],{"className":8512,"style":1554},[649,678,736],[572,8514,744],{"className":8515},[743],[572,8517,8519],{"className":8518},[661],[572,8520,8522],{"className":8521,"style":751},[665],[572,8523],{},[572,8525,611],{"className":8526},[757],[572,8528],{"className":8529,"style":762},[761],[572,8531,8533,8568],{"className":8532},[649],[572,8534,8536],{"className":8535},[649,653],[572,8537,8539],{"className":8538},[657],[572,8540,8542],{"className":8541},[661],[572,8543,8545,8553],{"className":8544,"style":666},[665],[572,8546,8547,8550],{"style":669},[572,8548],{"className":8549,"style":674},[673],[572,8551,600],{"className":8552,"style":679},[649,678],[572,8554,8555,8558],{"style":669},[572,8556],{"className":8557,"style":674},[673],[572,8559,8561],{"className":8560,"style":689},[688],[572,8562,8564],{"className":8563,"style":694},[693],[696,8565,8566],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8567],{"d":707},[572,8569,8571],{"className":8570},[711],[572,8572,8574,8594],{"className":8573},[657,715],[572,8575,8577,8591],{"className":8576},[661],[572,8578,8580],{"className":8579,"style":1680},[665],[572,8581,8582,8585],{"style":725},[572,8583],{"className":8584,"style":729},[673],[572,8586,8588],{"className":8587},[733,734,735,736],[572,8589,1524],{"className":8590,"style":1554},[649,678,736],[572,8592,744],{"className":8593},[743],[572,8595,8597],{"className":8596},[661],[572,8598,8600],{"className":8599,"style":751},[665],[572,8601],{},[572,8603,3314],{"className":8604},[2358]," statt ",[572,8607,8609,8647],{"className":8608},[575],[572,8610,8612],{"className":8611},[579],[581,8613,8614],{"xmlns":583},[585,8615,8616,8644],{},[588,8617,8618,8620,8630,8632,8642],{},[602,8619,3303],{"stretchy":2090},[591,8621,8622,8628],{},[594,8623,8624,8626],{"accent":596},[598,8625,872],{},[602,8627,604],{},[598,8629,1726],{},[602,8631,611],{"separator":596},[591,8633,8634,8640],{},[594,8635,8636,8638],{"accent":596},[598,8637,872],{},[602,8639,604],{},[598,8641,1726],{},[602,8643,3314],{"stretchy":2090},[629,8645,8646],{"encoding":631},"\\langle \\vec u_j, \\vec u_j \\rangle",[572,8648,8650],{"className":8649,"ariaHidden":596},[636],[572,8651,8653,8656,8659,8731,8734,8737,8809],{"className":8652},[640],[572,8654],{"className":8655,"style":6733},[644],[572,8657,3303],{"className":8658},[2282],[572,8660,8662,8697],{"className":8661},[649],[572,8663,8665],{"className":8664},[649,653],[572,8666,8668],{"className":8667},[657],[572,8669,8671],{"className":8670},[661],[572,8672,8674,8682],{"className":8673,"style":666},[665],[572,8675,8676,8679],{"style":669},[572,8677],{"className":8678,"style":674},[673],[572,8680,872],{"className":8681},[649,678],[572,8683,8684,8687],{"style":669},[572,8685],{"className":8686,"style":674},[673],[572,8688,8690],{"className":8689,"style":689},[688],[572,8691,8693],{"className":8692,"style":694},[693],[696,8694,8695],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8696],{"d":707},[572,8698,8700],{"className":8699},[711],[572,8701,8703,8723],{"className":8702},[657,715],[572,8704,8706,8720],{"className":8705},[661],[572,8707,8709],{"className":8708,"style":1790},[665],[572,8710,8711,8714],{"style":957},[572,8712],{"className":8713,"style":729},[673],[572,8715,8717],{"className":8716},[733,734,735,736],[572,8718,1726],{"className":8719,"style":1802},[649,678,736],[572,8721,744],{"className":8722},[743],[572,8724,8726],{"className":8725},[661],[572,8727,8729],{"className":8728,"style":1812},[665],[572,8730],{},[572,8732,611],{"className":8733},[757],[572,8735],{"className":8736,"style":762},[761],[572,8738,8740,8775],{"className":8739},[649],[572,8741,8743],{"className":8742},[649,653],[572,8744,8746],{"className":8745},[657],[572,8747,8749],{"className":8748},[661],[572,8750,8752,8760],{"className":8751,"style":666},[665],[572,8753,8754,8757],{"style":669},[572,8755],{"className":8756,"style":674},[673],[572,8758,872],{"className":8759},[649,678],[572,8761,8762,8765],{"style":669},[572,8763],{"className":8764,"style":674},[673],[572,8766,8768],{"className":8767,"style":689},[688],[572,8769,8771],{"className":8770,"style":694},[693],[696,8772,8773],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8774],{"d":707},[572,8776,8778],{"className":8777},[711],[572,8779,8781,8801],{"className":8780},[657,715],[572,8782,8784,8798],{"className":8783},[661],[572,8785,8787],{"className":8786,"style":1790},[665],[572,8788,8789,8792],{"style":957},[572,8790],{"className":8791,"style":729},[673],[572,8793,8795],{"className":8794},[733,734,735,736],[572,8796,1726],{"className":8797,"style":1802},[649,678,736],[572,8799,744],{"className":8800},[743],[572,8802,8804],{"className":8803},[661],[572,8805,8807],{"className":8806,"style":1812},[665],[572,8808],{},[572,8810,3314],{"className":8811},[2358]," verwenden.",[1296,8814,8815,8816,8921,8922,9028,9029,9322,9323,1288],{},"Den Nenner weglassen, obwohl mit den nicht normierten ",[572,8817,8819,8840],{"className":8818},[575],[572,8820,8822],{"className":8821},[579],[581,8823,8824],{"xmlns":583},[585,8825,8826,8838],{},[588,8827,8828],{},[591,8829,8830,8836],{},[594,8831,8832,8834],{"accent":596},[598,8833,872],{},[602,8835,604],{},[598,8837,1726],{},[629,8839,1729],{"encoding":631},[572,8841,8843],{"className":8842,"ariaHidden":596},[636],[572,8844,8846,8849],{"className":8845},[640],[572,8847],{"className":8848,"style":1739},[644],[572,8850,8852,8887],{"className":8851},[649],[572,8853,8855],{"className":8854},[649,653],[572,8856,8858],{"className":8857},[657],[572,8859,8861],{"className":8860},[661],[572,8862,8864,8872],{"className":8863,"style":666},[665],[572,8865,8866,8869],{"style":669},[572,8867],{"className":8868,"style":674},[673],[572,8870,872],{"className":8871},[649,678],[572,8873,8874,8877],{"style":669},[572,8875],{"className":8876,"style":674},[673],[572,8878,8880],{"className":8879,"style":689},[688],[572,8881,8883],{"className":8882,"style":694},[693],[696,8884,8885],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8886],{"d":707},[572,8888,8890],{"className":8889},[711],[572,8891,8893,8913],{"className":8892},[657,715],[572,8894,8896,8910],{"className":8895},[661],[572,8897,8899],{"className":8898,"style":1790},[665],[572,8900,8901,8904],{"style":957},[572,8902],{"className":8903,"style":729},[673],[572,8905,8907],{"className":8906},[733,734,735,736],[572,8908,1726],{"className":8909,"style":1802},[649,678,736],[572,8911,744],{"className":8912},[743],[572,8914,8916],{"className":8915},[661],[572,8917,8919],{"className":8918,"style":1812},[665],[572,8920],{}," gerechnet wird. Ohne Nenner geht es nur mit den normierten ",[572,8923,8925,8947],{"className":8924},[575],[572,8926,8928],{"className":8927},[579],[581,8929,8930],{"xmlns":583},[585,8931,8932,8944],{},[588,8933,8934],{},[591,8935,8936,8942],{},[594,8937,8938,8940],{"accent":596},[598,8939,1090],{},[602,8941,604],{},[598,8943,1726],{},[629,8945,8946],{"encoding":631},"\\vec w_j",[572,8948,8950],{"className":8949,"ariaHidden":596},[636],[572,8951,8953,8956],{"className":8952},[640],[572,8954],{"className":8955,"style":1739},[644],[572,8957,8959,8994],{"className":8958},[649],[572,8960,8962],{"className":8961},[649,653],[572,8963,8965],{"className":8964},[657],[572,8966,8968],{"className":8967},[661],[572,8969,8971,8979],{"className":8970,"style":666},[665],[572,8972,8973,8976],{"style":669},[572,8974],{"className":8975,"style":674},[673],[572,8977,1090],{"className":8978,"style":1146},[649,678],[572,8980,8981,8984],{"style":669},[572,8982],{"className":8983,"style":674},[673],[572,8985,8987],{"className":8986,"style":1155},[688],[572,8988,8990],{"className":8989,"style":694},[693],[696,8991,8992],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,8993],{"d":707},[572,8995,8997],{"className":8996},[711],[572,8998,9000,9020],{"className":8999},[657,715],[572,9001,9003,9017],{"className":9002},[661],[572,9004,9006],{"className":9005,"style":1790},[665],[572,9007,9008,9011],{"style":1177},[572,9009],{"className":9010,"style":729},[673],[572,9012,9014],{"className":9013},[733,734,735,736],[572,9015,1726],{"className":9016,"style":1802},[649,678,736],[572,9018,744],{"className":9019},[743],[572,9021,9023],{"className":9022},[661],[572,9024,9026],{"className":9025,"style":1812},[665],[572,9027],{},": Dann lautet der Abzug ",[572,9030,9032,9082],{"className":9031},[575],[572,9033,9035],{"className":9034},[579],[581,9036,9037],{"xmlns":583},[585,9038,9039,9079],{},[588,9040,9041,9043,9053,9055,9065,9067,9069],{},[602,9042,3303],{"stretchy":2090},[591,9044,9045,9051],{},[594,9046,9047,9049],{"accent":596},[598,9048,600],{},[602,9050,604],{},[598,9052,1524],{},[602,9054,611],{"separator":596},[591,9056,9057,9063],{},[594,9058,9059,9061],{"accent":596},[598,9060,1090],{},[602,9062,604],{},[598,9064,1726],{},[602,9066,3314],{"stretchy":2090},[3351,9068,3353],{},[591,9070,9071,9077],{},[594,9072,9073,9075],{"accent":596},[598,9074,1090],{},[602,9076,604],{},[598,9078,1726],{},[629,9080,9081],{"encoding":631},"\\langle \\vec v_k, \\vec w_j \\rangle\\, \\vec w_j",[572,9083,9085],{"className":9084,"ariaHidden":596},[636],[572,9086,9088,9091,9094,9166,9169,9172,9244,9247,9250],{"className":9087},[640],[572,9089],{"className":9090,"style":6733},[644],[572,9092,3303],{"className":9093},[2282],[572,9095,9097,9132],{"className":9096},[649],[572,9098,9100],{"className":9099},[649,653],[572,9101,9103],{"className":9102},[657],[572,9104,9106],{"className":9105},[661],[572,9107,9109,9117],{"className":9108,"style":666},[665],[572,9110,9111,9114],{"style":669},[572,9112],{"className":9113,"style":674},[673],[572,9115,600],{"className":9116,"style":679},[649,678],[572,9118,9119,9122],{"style":669},[572,9120],{"className":9121,"style":674},[673],[572,9123,9125],{"className":9124,"style":689},[688],[572,9126,9128],{"className":9127,"style":694},[693],[696,9129,9130],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,9131],{"d":707},[572,9133,9135],{"className":9134},[711],[572,9136,9138,9158],{"className":9137},[657,715],[572,9139,9141,9155],{"className":9140},[661],[572,9142,9144],{"className":9143,"style":1680},[665],[572,9145,9146,9149],{"style":725},[572,9147],{"className":9148,"style":729},[673],[572,9150,9152],{"className":9151},[733,734,735,736],[572,9153,1524],{"className":9154,"style":1554},[649,678,736],[572,9156,744],{"className":9157},[743],[572,9159,9161],{"className":9160},[661],[572,9162,9164],{"className":9163,"style":751},[665],[572,9165],{},[572,9167,611],{"className":9168},[757],[572,9170],{"className":9171,"style":762},[761],[572,9173,9175,9210],{"className":9174},[649],[572,9176,9178],{"className":9177},[649,653],[572,9179,9181],{"className":9180},[657],[572,9182,9184],{"className":9183},[661],[572,9185,9187,9195],{"className":9186,"style":666},[665],[572,9188,9189,9192],{"style":669},[572,9190],{"className":9191,"style":674},[673],[572,9193,1090],{"className":9194,"style":1146},[649,678],[572,9196,9197,9200],{"style":669},[572,9198],{"className":9199,"style":674},[673],[572,9201,9203],{"className":9202,"style":1155},[688],[572,9204,9206],{"className":9205,"style":694},[693],[696,9207,9208],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,9209],{"d":707},[572,9211,9213],{"className":9212},[711],[572,9214,9216,9236],{"className":9215},[657,715],[572,9217,9219,9233],{"className":9218},[661],[572,9220,9222],{"className":9221,"style":1790},[665],[572,9223,9224,9227],{"style":1177},[572,9225],{"className":9226,"style":729},[673],[572,9228,9230],{"className":9229},[733,734,735,736],[572,9231,1726],{"className":9232,"style":1802},[649,678,736],[572,9234,744],{"className":9235},[743],[572,9237,9239],{"className":9238},[661],[572,9240,9242],{"className":9241,"style":1812},[665],[572,9243],{},[572,9245,3314],{"className":9246},[2358],[572,9248],{"className":9249,"style":762},[761],[572,9251,9253,9288],{"className":9252},[649],[572,9254,9256],{"className":9255},[649,653],[572,9257,9259],{"className":9258},[657],[572,9260,9262],{"className":9261},[661],[572,9263,9265,9273],{"className":9264,"style":666},[665],[572,9266,9267,9270],{"style":669},[572,9268],{"className":9269,"style":674},[673],[572,9271,1090],{"className":9272,"style":1146},[649,678],[572,9274,9275,9278],{"style":669},[572,9276],{"className":9277,"style":674},[673],[572,9279,9281],{"className":9280,"style":1155},[688],[572,9282,9284],{"className":9283,"style":694},[693],[696,9285,9286],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,9287],{"d":707},[572,9289,9291],{"className":9290},[711],[572,9292,9294,9314],{"className":9293},[657,715],[572,9295,9297,9311],{"className":9296},[661],[572,9298,9300],{"className":9299,"style":1790},[665],[572,9301,9302,9305],{"style":1177},[572,9303],{"className":9304,"style":729},[673],[572,9306,9308],{"className":9307},[733,734,735,736],[572,9309,1726],{"className":9310,"style":1802},[649,678,736],[572,9312,744],{"className":9313},[743],[572,9315,9317],{"className":9316},[661],[572,9318,9320],{"className":9319,"style":1812},[665],[572,9321],{},", weil ",[572,9324,9326,9368],{"className":9325},[575],[572,9327,9329],{"className":9328},[579],[581,9330,9331],{"xmlns":583},[585,9332,9333,9365],{},[588,9334,9335,9337,9347,9349,9359,9361,9363],{},[602,9336,3303],{"stretchy":2090},[591,9338,9339,9345],{},[594,9340,9341,9343],{"accent":596},[598,9342,1090],{},[602,9344,604],{},[598,9346,1726],{},[602,9348,611],{"separator":596},[591,9350,9351,9357],{},[594,9352,9353,9355],{"accent":596},[598,9354,1090],{},[602,9356,604],{},[598,9358,1726],{},[602,9360,3314],{"stretchy":2090},[602,9362,1322],{},[606,9364,608],{},[629,9366,9367],{"encoding":631},"\\langle \\vec w_j, \\vec w_j \\rangle = 1",[572,9369,9371,9542],{"className":9370,"ariaHidden":596},[636],[572,9372,9374,9377,9380,9452,9455,9458,9530,9533,9536,9539],{"className":9373},[640],[572,9375],{"className":9376,"style":6733},[644],[572,9378,3303],{"className":9379},[2282],[572,9381,9383,9418],{"className":9382},[649],[572,9384,9386],{"className":9385},[649,653],[572,9387,9389],{"className":9388},[657],[572,9390,9392],{"className":9391},[661],[572,9393,9395,9403],{"className":9394,"style":666},[665],[572,9396,9397,9400],{"style":669},[572,9398],{"className":9399,"style":674},[673],[572,9401,1090],{"className":9402,"style":1146},[649,678],[572,9404,9405,9408],{"style":669},[572,9406],{"className":9407,"style":674},[673],[572,9409,9411],{"className":9410,"style":1155},[688],[572,9412,9414],{"className":9413,"style":694},[693],[696,9415,9416],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,9417],{"d":707},[572,9419,9421],{"className":9420},[711],[572,9422,9424,9444],{"className":9423},[657,715],[572,9425,9427,9441],{"className":9426},[661],[572,9428,9430],{"className":9429,"style":1790},[665],[572,9431,9432,9435],{"style":1177},[572,9433],{"className":9434,"style":729},[673],[572,9436,9438],{"className":9437},[733,734,735,736],[572,9439,1726],{"className":9440,"style":1802},[649,678,736],[572,9442,744],{"className":9443},[743],[572,9445,9447],{"className":9446},[661],[572,9448,9450],{"className":9449,"style":1812},[665],[572,9451],{},[572,9453,611],{"className":9454},[757],[572,9456],{"className":9457,"style":762},[761],[572,9459,9461,9496],{"className":9460},[649],[572,9462,9464],{"className":9463},[649,653],[572,9465,9467],{"className":9466},[657],[572,9468,9470],{"className":9469},[661],[572,9471,9473,9481],{"className":9472,"style":666},[665],[572,9474,9475,9478],{"style":669},[572,9476],{"className":9477,"style":674},[673],[572,9479,1090],{"className":9480,"style":1146},[649,678],[572,9482,9483,9486],{"style":669},[572,9484],{"className":9485,"style":674},[673],[572,9487,9489],{"className":9488,"style":1155},[688],[572,9490,9492],{"className":9491,"style":694},[693],[696,9493,9494],{"xmlns":698,"width":699,"height":700,"style":701,"viewBox":702,"preserveAspectRatio":703},[705,9495],{"d":707},[572,9497,9499],{"className":9498},[711],[572,9500,9502,9522],{"className":9501},[657,715],[572,9503,9505,9519],{"className":9504},[661],[572,9506,9508],{"className":9507,"style":1790},[665],[572,9509,9510,9513],{"style":1177},[572,9511],{"className":9512,"style":729},[673],[572,9514,9516],{"className":9515},[733,734,735,736],[572,9517,1726],{"className":9518,"style":1802},[649,678,736],[572,9520,744],{"className":9521},[743],[572,9523,9525],{"className":9524},[661],[572,9526,9528],{"className":9527,"style":1812},[665],[572,9529],{},[572,9531,3314],{"className":9532},[2358],[572,9534],{"className":9535,"style":1421},[761],[572,9537,1322],{"className":9538},[1425],[572,9540],{"className":9541,"style":1421},[761],[572,9543,9545,9548],{"className":9544},[640],[572,9546],{"className":9547,"style":3284},[644],[572,9549,608],{"className":9550},[649],[1296,9552,9553],{},"Das Normieren am Ende vergessen, wenn eine Orthonormalbasis verlangt ist.",{"title":9555,"searchDepth":9556,"depth":9556,"links":9557},"",2,[9558,9559,9560],{"id":561,"depth":9556,"text":562},{"id":3513,"depth":9556,"text":3514},{"id":8066,"depth":9556,"text":8067},[9562,9564,9566,9568,9571,9573,9576,9579,9582,9584,9586,9588,9590,9593,9596],{"lhs":9563,"rhs":2951},"dot([a, b, c], [p, q, r] - dot([p, q, r], [a, b, c])\u002Fdot([a, b, c], [a, b, c]) * [a, b, c])",{"lhs":9565,"rhs":5940},"dot([1, 0, 1], [1, 1, 0]) \u002F dot([1, 1, 0], [1, 1, 0])",{"lhs":9567,"rhs":5940},"1 - 1\u002F2*1",{"lhs":9569,"rhs":9570},"0 - 1\u002F2*1","-1\u002F2",{"lhs":9572,"rhs":5940},"dot([0, 1, 1], [1, 1, 0]) \u002F 2",{"lhs":9574,"rhs":9575},"dot([0, 1, 1], [0.5, -0.5, 1]) \u002F dot([0.5, -0.5, 1], [0.5, -0.5, 1])","1\u002F3",{"lhs":9577,"rhs":9578},"0 - 1\u002F2*1 - 1\u002F3*0.5","-2\u002F3",{"lhs":9580,"rhs":9581},"1 - 1\u002F2*1 - 1\u002F3*(-0.5)","2\u002F3",{"lhs":9583,"rhs":9581},"1 - 1\u002F2*0 - 1\u002F3*1",{"lhs":9585,"rhs":2951},"dot([1, 1, 0], [0.5, -0.5, 1])",{"lhs":9587,"rhs":2951},"dot([1, 1, 0], [-2\u002F3, 2\u002F3, 2\u002F3])",{"lhs":9589,"rhs":2951},"dot([0.5, -0.5, 1], [-2\u002F3, 2\u002F3, 2\u002F3])",{"lhs":9591,"rhs":9592},"norm([1, 1, 0])","sqrt(2)",{"lhs":9594,"rhs":9595},"norm([1, -1, 2])","sqrt(6)",{"lhs":9597,"rhs":9598},"norm([-1, 1, 1])","sqrt(3)","\\vec v_1, \\ldots, \\vec v_n \\text{ linear unabhängig}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec v_1, \\ldots, \\vec v_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">linear unabhängig\u003C\u002Fspan>",null,"md","gram-schmidt","\\vec u_k = \\vec v_k - \\sum_{j=1}^{k-1} \\frac{\\langle \\vec v_k, \\vec u_j \\rangle}{\\langle \\vec u_j, \\vec u_j \\rangle}\\, \\vec u_j, \\qquad \\vec w_k = \\frac{\\vec u_k}{\\lVert \\vec u_k \\rVert}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>j\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmrow>\u003Cmo stretchy=\"false\">⟨\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">⟩\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmo stretchy=\"false\">⟨\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">⟩\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>w\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmrow>\u003Cmo stretchy=\"false\">∥\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">∥\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec u_k = \\vec v_k - \\sum_{j=1}^{k-1} \\frac{\\langle \\vec v_k, \\vec u_j \\rangle}{\\langle \\vec u_j, \\vec u_j \\rangle}\\, \\vec u_j, \\qquad \\vec w_k = \\frac{\\vec u_k}{\\lVert \\vec u_k \\rVert}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:3.2499em;vertical-align:-1.4138em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.8361em;\">\u003Cspan style=\"top:-1.8723em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4138em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.427em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen\">⟨\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">⟩\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen\">⟨\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">⟩\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9721em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0269em;\">w\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.327em;vertical-align:-0.936em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.391em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen\">∥\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">∥\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.936em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgram-schmidt-verfahren",[],[9612,9613,9614,9615],"vector-projection","orthogonal-matrix","dot-product","linear-independence",{"title":548,"description":9555},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgram-schmidt-verfahren","Man zieht von jedem Vektor seine Projektionen auf die bereits orthogonalisierten Vektoren ab und normiert danach.",[9620,9621,9622,9623],"orthogonalisierung","orthonormalbasis","skalarprodukt","projektion",[9625,9628,9631,9635,9639],{"symbol":632,"meaning":9626,"symbolHtml":9627},"gegebene linear unabhängige Vektoren","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec v_1, \\ldots, \\vec v_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3119,"meaning":9629,"symbolHtml":9630},"k-ter orthogonalisierter Vektor, beginnend mit u₁ = v₁","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec u_k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":9632,"meaning":9633,"symbolHtml":9634},"\\vec w_k","k-ter normierter Vektor der Orthonormalbasis","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>w\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec w_k\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0269em;\">w\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":9636,"meaning":9637,"symbolHtml":9638},"\\langle \\cdot, \\cdot \\rangle","Skalarprodukt, im Rⁿ das Standardskalarprodukt","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">⟨\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">⟩\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\langle \\cdot, \\cdot \\rangle\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">⟨\u003C\u002Fspan>\u003Cspan class=\"mord\">⋅\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">⋅\u003C\u002Fspan>\u003Cspan class=\"mclose\">⟩\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":9640,"meaning":9641,"symbolHtml":9642},"\\lVert \\vec u_k \\rVert","Länge (Norm) von u_k","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">∥\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">∥\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lVert \\vec u_k \\rVert\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">∥\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">∥\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","xqyw4NGVQhhXvNLi1i7HQd9FdSARbxVSlcMNfMjozR0",[9645,9648,9651,9654],{"stem":9646,"title":9647,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Flineare-unabhaengigkeit","Lineare Unabhängigkeit",{"stem":9649,"title":9650,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Forthogonale-matrix","Orthogonale Matrix",{"stem":9652,"title":9653,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Forthogonale-projektion","Orthogonale Projektion",{"stem":9655,"title":9656,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fskalarprodukt","Skalarprodukt",1793824278248]