[{"data":1,"prerenderedAt":4035},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fkonditionszahl":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fkonditionszahl":4022},[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":391,"checks":3945,"conditions":3977,"conditionsHtml":3978,"deprecated":3979,"description":3939,"extension":3980,"figure":3979,"figureCaption":3979,"figureHtml":3979,"formulaId":3981,"latex":3982,"latexHtml":3983,"level":3984,"meta":3985,"navigation":3986,"path":3987,"redirectFrom":3988,"related":3989,"seo":3994,"stem":3995,"subject":581,"summary":3996,"tags":3997,"variables":4002,"__hash__":4021},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fnumerics\u002Fkonditionszahl.md","Konditionszahl",[550,551,552,553,554],"Kondition einer Matrix","Konditionszahl Matrix","cond(A)","schlecht konditioniert","Fehlerverstärkung lineares Gleichungssystem",{"type":556,"value":557,"toc":3938},"minimark",[558,563,895,1271,1899,1906,1910,2398,2660,2837,3595,3599],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,570,571,653,654,690,691,813,814,865,866,894],"p",{},"Die ",[568,569,548],"strong",{}," misst, wie empfindlich die Lösung eines linearen Gleichungssystems ",[572,573,576,609],"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",[585,586,587,604],"semantics",{},[588,589,590,594,597,601],"mrow",{},[591,592,593],"mi",{},"A",[591,595,596],{},"x",[598,599,600],"mo",{},"=",[591,602,603],{},"b",[605,606,608],"annotation",{"encoding":607},"application\u002Fx-tex","Ax = b",[572,610,614,643],{"className":611,"ariaHidden":613},[612],"katex-html","true",[572,615,618,623,628,631,636,640],{"className":616},[617],"base",[572,619],{"className":620,"style":622},[621],"strut","height:0.6833em;",[572,624,593],{"className":625},[626,627],"mord","mathnormal",[572,629,596],{"className":630},[626,627],[572,632],{"className":633,"style":635},[634],"mspace","margin-right:0.2778em;",[572,637,600],{"className":638},[639],"mrel",[572,641],{"className":642,"style":635},[634],[572,644,646,650],{"className":645},[617],[572,647],{"className":648,"style":649},[621],"height:0.6944em;",[572,651,603],{"className":652},[626,627]," auf Störungen der Daten reagiert. Ändert sich die rechte Seite um ",[572,655,657,675],{"className":656},[575],[572,658,660],{"className":659},[579],[581,661,662],{"xmlns":583},[585,663,664,672],{},[588,665,666,670],{},[591,667,669],{"mathvariant":668},"normal","Δ",[591,671,603],{},[605,673,674],{"encoding":607},"\\Delta b",[572,676,678],{"className":677,"ariaHidden":613},[612],[572,679,681,684,687],{"className":680},[617],[572,682],{"className":683,"style":649},[621],[572,685,669],{"className":686},[626],[572,688,603],{"className":689},[626,627],", ändert sich die Lösung um ",[572,692,694,730],{"className":693},[575],[572,695,697],{"className":696},[579],[581,698,699],{"xmlns":583},[585,700,701,727],{},[588,702,703,705,707,709,723,725],{},[591,704,669],{"mathvariant":668},[591,706,596],{},[598,708,600],{},[710,711,712,714],"msup",{},[591,713,593],{},[588,715,716,719],{},[598,717,718],{},"−",[720,721,722],"mn",{},"1",[591,724,669],{"mathvariant":668},[591,726,603],{},[605,728,729],{"encoding":607},"\\Delta x = A^{-1}\\Delta b",[572,731,733,754],{"className":732,"ariaHidden":613},[612],[572,734,736,739,742,745,748,751],{"className":735},[617],[572,737],{"className":738,"style":622},[621],[572,740,669],{"className":741},[626],[572,743,596],{"className":744},[626,627],[572,746],{"className":747,"style":635},[634],[572,749,600],{"className":750},[639],[572,752],{"className":753,"style":635},[634],[572,755,757,761,807,810],{"className":756},[617],[572,758],{"className":759,"style":760},[621],"height:0.8141em;",[572,762,764,767],{"className":763},[626],[572,765,593],{"className":766},[626,627],[572,768,771],{"className":769},[770],"msupsub",[572,772,775],{"className":773},[774],"vlist-t",[572,776,779],{"className":777},[778],"vlist-r",[572,780,783],{"className":781,"style":760},[782],"vlist",[572,784,786,791],{"style":785},"top:-3.063em;margin-right:0.05em;",[572,787],{"className":788,"style":790},[789],"pstrut","height:2.7em;",[572,792,798],{"className":793},[794,795,796,797],"sizing","reset-size6","size3","mtight",[572,799,801,804],{"className":800},[626,797],[572,802,718],{"className":803},[626,797],[572,805,722],{"className":806},[626,797],[572,808,669],{"className":809},[626],[572,811,603],{"className":812},[626,627],". Daraus folgt die Abschätzung oben: Der relative Fehler der Lösung ist höchstens ",[572,815,817,841],{"className":816},[575],[572,818,820],{"className":819},[579],[581,821,822],{"xmlns":583},[585,823,824,838],{},[588,825,826,829,833,835],{},[591,827,828],{},"κ",[598,830,832],{"stretchy":831},"false","(",[591,834,593],{},[598,836,837],{"stretchy":831},")",[605,839,840],{"encoding":607},"\\kappa(A)",[572,842,844],{"className":843,"ariaHidden":613},[612],[572,845,847,851,854,858,861],{"className":846},[617],[572,848],{"className":849,"style":850},[621],"height:1em;vertical-align:-0.25em;",[572,852,828],{"className":853},[626,627],[572,855,832],{"className":856},[857],"mopen",[572,859,593],{"className":860},[626,627],[572,862,837],{"className":863},[864],"mclose","-mal so groß wie der relative Fehler der Daten. Eine ähnliche Abschätzung gilt für Störungen in ",[572,867,869,882],{"className":868},[575],[572,870,872],{"className":871},[579],[581,873,874],{"xmlns":583},[585,875,876,880],{},[588,877,878],{},[591,879,593],{},[605,881,593],{"encoding":607},[572,883,885],{"className":884,"ariaHidden":613},[612],[572,886,888,891],{"className":887},[617],[572,889],{"className":890,"style":622},[621],[572,892,593],{"className":893},[626,627],".",[896,897,898,970,1101,1150],"ul",{},[899,900,901,902,894],"li",{},"Für jede induzierte Matrixnorm gilt ",[572,903,905,930],{"className":904},[575],[572,906,908],{"className":907},[579],[581,909,910],{"xmlns":583},[585,911,912,927],{},[588,913,914,916,918,920,922,925],{},[591,915,828],{},[598,917,832],{"stretchy":831},[591,919,593],{},[598,921,837],{"stretchy":831},[598,923,924],{},"≥",[720,926,722],{},[605,928,929],{"encoding":607},"\\kappa(A) \\geq 1",[572,931,933,960],{"className":932,"ariaHidden":613},[612],[572,934,936,939,942,945,948,951,954,957],{"className":935},[617],[572,937],{"className":938,"style":850},[621],[572,940,828],{"className":941},[626,627],[572,943,832],{"className":944},[857],[572,946,593],{"className":947},[626,627],[572,949,837],{"className":950},[864],[572,952],{"className":953,"style":635},[634],[572,955,924],{"className":956},[639],[572,958],{"className":959,"style":635},[634],[572,961,963,967],{"className":962},[617],[572,964],{"className":965,"style":966},[621],"height:0.6444em;",[572,968,722],{"className":969},[626],[899,971,972,1015,1016,1044,1045,1048,1049,894],{},[572,973,975,994],{"className":974},[575],[572,976,978],{"className":977},[579],[581,979,980],{"xmlns":583},[585,981,982,992],{},[588,983,984,986,988,990],{},[591,985,828],{},[598,987,832],{"stretchy":831},[591,989,593],{},[598,991,837],{"stretchy":831},[605,993,840],{"encoding":607},[572,995,997],{"className":996,"ariaHidden":613},[612],[572,998,1000,1003,1006,1009,1012],{"className":999},[617],[572,1001],{"className":1002,"style":850},[621],[572,1004,828],{"className":1005},[626,627],[572,1007,832],{"className":1008},[857],[572,1010,593],{"className":1011},[626,627],[572,1013,837],{"className":1014},[864]," nahe ",[572,1017,1019,1032],{"className":1018},[575],[572,1020,1022],{"className":1021},[579],[581,1023,1024],{"xmlns":583},[585,1025,1026,1030],{},[588,1027,1028],{},[720,1029,722],{},[605,1031,722],{"encoding":607},[572,1033,1035],{"className":1034,"ariaHidden":613},[612],[572,1036,1038,1041],{"className":1037},[617],[572,1039],{"className":1040,"style":966},[621],[572,1042,722],{"className":1043},[626],": ",[568,1046,1047],{},"gut konditioniert",". Orthogonale Matrizen haben in der euklidischen Norm ",[572,1050,1052,1070],{"className":1051},[575],[572,1053,1055],{"className":1054},[579],[581,1056,1057],{"xmlns":583},[585,1058,1059,1067],{},[588,1060,1061,1063,1065],{},[591,1062,828],{},[598,1064,600],{},[720,1066,722],{},[605,1068,1069],{"encoding":607},"\\kappa = 1",[572,1071,1073,1092],{"className":1072,"ariaHidden":613},[612],[572,1074,1076,1080,1083,1086,1089],{"className":1075},[617],[572,1077],{"className":1078,"style":1079},[621],"height:0.4306em;",[572,1081,828],{"className":1082},[626,627],[572,1084],{"className":1085,"style":635},[634],[572,1087,600],{"className":1088},[639],[572,1090],{"className":1091,"style":635},[634],[572,1093,1095,1098],{"className":1094},[617],[572,1096],{"className":1097,"style":966},[621],[572,1099,722],{"className":1100},[626],[899,1102,1103,1146,1147,1149],{},[572,1104,1106,1125],{"className":1105},[575],[572,1107,1109],{"className":1108},[579],[581,1110,1111],{"xmlns":583},[585,1112,1113,1123],{},[588,1114,1115,1117,1119,1121],{},[591,1116,828],{},[598,1118,832],{"stretchy":831},[591,1120,593],{},[598,1122,837],{"stretchy":831},[605,1124,840],{"encoding":607},[572,1126,1128],{"className":1127,"ariaHidden":613},[612],[572,1129,1131,1134,1137,1140,1143],{"className":1130},[617],[572,1132],{"className":1133,"style":850},[621],[572,1135,828],{"className":1136},[626,627],[572,1138,832],{"className":1139},[857],[572,1141,593],{"className":1142},[626,627],[572,1144,837],{"className":1145},[864]," groß: ",[568,1148,553],{},". Kleine Rundungs- oder Messfehler können die Lösung stark verfälschen.",[899,1151,1152,1153,1270],{},"Faustregel: Man verliert etwa ",[572,1154,1156,1190],{"className":1155},[575],[572,1157,1159],{"className":1158},[579],[581,1160,1161],{"xmlns":583},[585,1162,1163,1187],{},[588,1164,1165,1179,1181,1183,1185],{},[1166,1167,1168,1176],"msub",{},[588,1169,1170,1173],{},[591,1171,1172],{},"log",[598,1174,1175],{},"⁡",[720,1177,1178],{},"10",[591,1180,828],{},[598,1182,832],{"stretchy":831},[591,1184,593],{},[598,1186,837],{"stretchy":831},[605,1188,1189],{"encoding":607},"\\log_{10} \\kappa(A)",[572,1191,1193],{"className":1192,"ariaHidden":613},[612],[572,1194,1196,1199,1254,1258,1261,1264,1267],{"className":1195},[617],[572,1197],{"className":1198,"style":850},[621],[572,1200,1203,1211],{"className":1201},[1202],"mop",[572,1204,1206,1207],{"className":1205},[1202],"lo",[572,1208,1210],{"style":1209},"margin-right:0.0139em;","g",[572,1212,1214],{"className":1213},[770],[572,1215,1218,1245],{"className":1216},[774,1217],"vlist-t2",[572,1219,1221,1240],{"className":1220},[778],[572,1222,1225],{"className":1223,"style":1224},[782],"height:0.207em;",[572,1226,1228,1231],{"style":1227},"top:-2.4559em;margin-right:0.05em;",[572,1229],{"className":1230,"style":790},[789],[572,1232,1234],{"className":1233},[794,795,796,797],[572,1235,1237],{"className":1236},[626,797],[572,1238,1178],{"className":1239},[626,797],[572,1241,1244],{"className":1242},[1243],"vlist-s","​",[572,1246,1248],{"className":1247},[778],[572,1249,1252],{"className":1250,"style":1251},[782],"height:0.2441em;",[572,1253],{},[572,1255],{"className":1256,"style":1257},[634],"margin-right:0.1667em;",[572,1259,828],{"className":1260},[626,627],[572,1262,832],{"className":1263},[857],[572,1265,593],{"className":1266},[626,627],[572,1268,837],{"className":1269},[864]," Dezimalstellen an Genauigkeit.",[564,1272,1273,1274,1277,1278,1563,1564,1898],{},"Der Wert hängt von der Norm ab. Häufig verwendet man die ",[568,1275,1276],{},"Zeilensummennorm"," ",[572,1279,1281,1343],{"className":1280},[575],[572,1282,1284],{"className":1283},[579],[581,1285,1286],{"xmlns":583},[585,1287,1288,1340],{},[588,1289,1290,1293,1295,1302,1304,1316,1324,1327,1338],{},[591,1291,1292],{"mathvariant":668},"∥",[591,1294,593],{},[1166,1296,1297,1299],{},[591,1298,1292],{"mathvariant":668},[591,1300,1301],{"mathvariant":668},"∞",[598,1303,600],{},[1166,1305,1306,1313],{},[588,1307,1308,1311],{},[591,1309,1310],{},"max",[598,1312,1175],{},[591,1314,1315],{},"i",[1166,1317,1318,1321],{},[598,1319,1320],{},"∑",[591,1322,1323],{},"j",[591,1325,1326],{"mathvariant":668},"∣",[1166,1328,1329,1332],{},[591,1330,1331],{},"a",[588,1333,1334,1336],{},[591,1335,1315],{},[591,1337,1323],{},[591,1339,1326],{"mathvariant":668},[605,1341,1342],{"encoding":607},"\\|A\\|_\\infty = \\max_i \\sum_j |a_{ij}|",[572,1344,1346,1410],{"className":1345,"ariaHidden":613},[612],[572,1347,1349,1352,1355,1358,1401,1404,1407],{"className":1348},[617],[572,1350],{"className":1351,"style":850},[621],[572,1353,1292],{"className":1354},[626],[572,1356,593],{"className":1357},[626,627],[572,1359,1361,1364],{"className":1360},[626],[572,1362,1292],{"className":1363},[626],[572,1365,1367],{"className":1366},[770],[572,1368,1370,1392],{"className":1369},[774,1217],[572,1371,1373,1389],{"className":1372},[778],[572,1374,1377],{"className":1375,"style":1376},[782],"height:0.1514em;",[572,1378,1380,1383],{"style":1379},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[572,1381],{"className":1382,"style":790},[789],[572,1384,1386],{"className":1385},[794,795,796,797],[572,1387,1301],{"className":1388},[626,797],[572,1390,1244],{"className":1391},[1243],[572,1393,1395],{"className":1394},[778],[572,1396,1399],{"className":1397,"style":1398},[782],"height:0.15em;",[572,1400],{},[572,1402],{"className":1403,"style":635},[634],[572,1405,600],{"className":1406},[639],[572,1408],{"className":1409,"style":635},[634],[572,1411,1413,1417,1459,1462,1509,1512,1515,1560],{"className":1412},[617],[572,1414],{"className":1415,"style":1416},[621],"height:1.1858em;vertical-align:-0.4358em;",[572,1418,1420,1423],{"className":1419},[1202],[572,1421,1310],{"className":1422},[1202],[572,1424,1426],{"className":1425},[770],[572,1427,1429,1451],{"className":1428},[774,1217],[572,1430,1432,1448],{"className":1431},[778],[572,1433,1436],{"className":1434,"style":1435},[782],"height:0.3117em;",[572,1437,1439,1442],{"style":1438},"top:-2.55em;margin-right:0.05em;",[572,1440],{"className":1441,"style":790},[789],[572,1443,1445],{"className":1444},[794,795,796,797],[572,1446,1315],{"className":1447},[626,627,797],[572,1449,1244],{"className":1450},[1243],[572,1452,1454],{"className":1453},[778],[572,1455,1457],{"className":1456,"style":1398},[782],[572,1458],{},[572,1460],{"className":1461,"style":1257},[634],[572,1463,1465,1471],{"className":1464},[1202],[572,1466,1320],{"className":1467,"style":1470},[1202,1468,1469],"op-symbol","small-op","position:relative;top:0em;",[572,1472,1474],{"className":1473},[770],[572,1475,1477,1500],{"className":1476},[774,1217],[572,1478,1480,1497],{"className":1479},[778],[572,1481,1484],{"className":1482,"style":1483},[782],"height:0.162em;",[572,1485,1487,1490],{"style":1486},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[572,1488],{"className":1489,"style":790},[789],[572,1491,1493],{"className":1492},[794,795,796,797],[572,1494,1323],{"className":1495,"style":1496},[626,627,797],"margin-right:0.0572em;",[572,1498,1244],{"className":1499},[1243],[572,1501,1503],{"className":1502},[778],[572,1504,1507],{"className":1505,"style":1506},[782],"height:0.4358em;",[572,1508],{},[572,1510],{"className":1511,"style":1257},[634],[572,1513,1326],{"className":1514},[626],[572,1516,1518,1521],{"className":1517},[626],[572,1519,1331],{"className":1520},[626,627],[572,1522,1524],{"className":1523},[770],[572,1525,1527,1551],{"className":1526},[774,1217],[572,1528,1530,1548],{"className":1529},[778],[572,1531,1533],{"className":1532,"style":1435},[782],[572,1534,1535,1538],{"style":1379},[572,1536],{"className":1537,"style":790},[789],[572,1539,1541],{"className":1540},[794,795,796,797],[572,1542,1544],{"className":1543},[626,797],[572,1545,1547],{"className":1546,"style":1496},[626,627,797],"ij",[572,1549,1244],{"className":1550},[1243],[572,1552,1554],{"className":1553},[778],[572,1555,1558],{"className":1556,"style":1557},[782],"height:0.2861em;",[572,1559],{},[572,1561,1326],{"className":1562},[626]," oder die Spektralnorm. Für symmetrische Matrizen ist ",[572,1565,1567,1627],{"className":1566},[575],[572,1568,1570],{"className":1569},[579],[581,1571,1572],{"xmlns":583},[585,1573,1574,1624],{},[588,1575,1576,1583,1585,1587,1589,1591],{},[1166,1577,1578,1580],{},[591,1579,828],{},[720,1581,1582],{},"2",[598,1584,832],{"stretchy":831},[591,1586,593],{},[598,1588,837],{"stretchy":831},[598,1590,600],{},[1592,1593,1594,1609],"mfrac",{},[588,1595,1596,1598,1607],{},[591,1597,1326],{"mathvariant":668},[1166,1599,1600,1603,1605],{},[591,1601,1602],{},"λ",[591,1604,1310],{},[598,1606,1175],{},[591,1608,1326],{"mathvariant":668},[588,1610,1611,1613,1622],{},[591,1612,1326],{"mathvariant":668},[1166,1614,1615,1617,1620],{},[591,1616,1602],{},[591,1618,1619],{},"min",[598,1621,1175],{},[591,1623,1326],{"mathvariant":668},[605,1625,1626],{"encoding":607},"\\kappa_2(A) = \\frac{|\\lambda_{\\max}|}{|\\lambda_{\\min}|}",[572,1628,1630,1695],{"className":1629,"ariaHidden":613},[612],[572,1631,1633,1636,1677,1680,1683,1686,1689,1692],{"className":1632},[617],[572,1634],{"className":1635,"style":850},[621],[572,1637,1639,1642],{"className":1638},[626],[572,1640,828],{"className":1641},[626,627],[572,1643,1645],{"className":1644},[770],[572,1646,1648,1669],{"className":1647},[774,1217],[572,1649,1651,1666],{"className":1650},[778],[572,1652,1655],{"className":1653,"style":1654},[782],"height:0.3011em;",[572,1656,1657,1660],{"style":1379},[572,1658],{"className":1659,"style":790},[789],[572,1661,1663],{"className":1662},[794,795,796,797],[572,1664,1582],{"className":1665},[626,797],[572,1667,1244],{"className":1668},[1243],[572,1670,1672],{"className":1671},[778],[572,1673,1675],{"className":1674,"style":1398},[782],[572,1676],{},[572,1678,832],{"className":1679},[857],[572,1681,593],{"className":1682},[626,627],[572,1684,837],{"className":1685},[864],[572,1687],{"className":1688,"style":635},[634],[572,1690,600],{"className":1691},[639],[572,1693],{"className":1694,"style":635},[634],[572,1696,1698,1702],{"className":1697},[617],[572,1699],{"className":1700,"style":1701},[621],"height:1.53em;vertical-align:-0.52em;",[572,1703,1705,1709,1895],{"className":1704},[626],[572,1706],{"className":1707},[857,1708],"nulldelimiter",[572,1710,1712],{"className":1711},[1592],[572,1713,1715,1886],{"className":1714},[774,1217],[572,1716,1718,1883],{"className":1717},[778],[572,1719,1722,1801,1812],{"className":1720,"style":1721},[782],"height:1.01em;",[572,1723,1725,1729],{"style":1724},"top:-2.655em;",[572,1726],{"className":1727,"style":1728},[789],"height:3em;",[572,1730,1732],{"className":1731},[794,795,796,797],[572,1733,1735,1738,1798],{"className":1734},[626,797],[572,1736,1326],{"className":1737},[626,797],[572,1739,1741,1744],{"className":1740},[626,797],[572,1742,1602],{"className":1743},[626,627,797],[572,1745,1747],{"className":1746},[770],[572,1748,1750,1789],{"className":1749},[774,1217],[572,1751,1753,1786],{"className":1752},[778],[572,1754,1757],{"className":1755,"style":1756},[782],"height:0.334em;",[572,1758,1760,1764],{"style":1759},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[572,1761],{"className":1762,"style":1763},[789],"height:2.5em;",[572,1765,1769],{"className":1766},[794,1767,1768,797],"reset-size3","size1",[572,1770,1772],{"className":1771},[626,797],[572,1773,1775,1779,1782],{"className":1774},[1202,797],[572,1776,1778],{"className":1777},[797],"m",[572,1780,1315],{"className":1781},[797],[572,1783,1785],{"className":1784},[797],"n",[572,1787,1244],{"className":1788},[1243],[572,1790,1792],{"className":1791},[778],[572,1793,1796],{"className":1794,"style":1795},[782],"height:0.143em;",[572,1797],{},[572,1799,1326],{"className":1800},[626,797],[572,1802,1804,1807],{"style":1803},"top:-3.23em;",[572,1805],{"className":1806,"style":1728},[789],[572,1808],{"className":1809,"style":1811},[1810],"frac-line","border-bottom-width:0.04em;",[572,1813,1815,1818],{"style":1814},"top:-3.485em;",[572,1816],{"className":1817,"style":1728},[789],[572,1819,1821],{"className":1820},[794,795,796,797],[572,1822,1824,1827,1880],{"className":1823},[626,797],[572,1825,1326],{"className":1826},[626,797],[572,1828,1830,1833],{"className":1829},[626,797],[572,1831,1602],{"className":1832},[626,627,797],[572,1834,1836],{"className":1835},[770],[572,1837,1839,1872],{"className":1838},[774,1217],[572,1840,1842,1869],{"className":1841},[778],[572,1843,1846],{"className":1844,"style":1845},[782],"height:0.1645em;",[572,1847,1848,1851],{"style":1759},[572,1849],{"className":1850,"style":1763},[789],[572,1852,1854],{"className":1853},[794,1767,1768,797],[572,1855,1857],{"className":1856},[626,797],[572,1858,1860,1863,1866],{"className":1859},[1202,797],[572,1861,1778],{"className":1862},[797],[572,1864,1331],{"className":1865},[797],[572,1867,596],{"className":1868},[797],[572,1870,1244],{"className":1871},[1243],[572,1873,1875],{"className":1874},[778],[572,1876,1878],{"className":1877,"style":1795},[782],[572,1879],{},[572,1881,1326],{"className":1882},[626,797],[572,1884,1244],{"className":1885},[1243],[572,1887,1889],{"className":1888},[778],[572,1890,1893],{"className":1891,"style":1892},[782],"height:0.52em;",[572,1894],{},[572,1896],{"className":1897},[864,1708],", der Quotient der betragsgrößten und betragskleinsten Eigenwerte.",[564,1900,1901,1902,1905],{},"Die Kondition ist eine Eigenschaft des ",[568,1903,1904],{},"Problems",", nicht des Lösungsverfahrens. Auch das beste Verfahren kann die Fehlerverstärkung eines schlecht konditionierten Problems nicht beseitigen.",[559,1907,1909],{"id":1908},"beispiele","Beispiele",[572,1911,1914],{"className":1912},[1913],"katex-display",[572,1915,1917,2043],{"className":1916},[575],[572,1918,1920],{"className":1919},[579],[581,1921,1923],{"xmlns":583,"display":1922},"block",[585,1924,1925,2040],{},[588,1926,1927,1929,1931,1976,1979,1982,1992,1994],{},[591,1928,593],{},[598,1930,600],{},[588,1932,1933,1935,1974],{},[598,1934,832],{"fence":613},[1936,1937,1941,1959],"mtable",{"rowspacing":1938,"columnalign":1939,"columnspacing":1940},"0.16em","center center","1em",[1942,1943,1944,1953],"mtr",{},[1945,1946,1947],"mtd",{},[1948,1949,1951],"mstyle",{"scriptlevel":1950,"displaystyle":831},"0",[720,1952,722],{},[1945,1954,1955],{},[1948,1956,1957],{"scriptlevel":1950,"displaystyle":831},[720,1958,722],{},[1942,1960,1961,1967],{},[1945,1962,1963],{},[1948,1964,1965],{"scriptlevel":1950,"displaystyle":831},[720,1966,722],{},[1945,1968,1969],{},[1948,1970,1971],{"scriptlevel":1950,"displaystyle":831},[720,1972,1973],{},"1,01",[598,1975,837],{"fence":613},[598,1977,1978],{"separator":613},",",[634,1980],{"width":1981},"2em",[710,1983,1984,1986],{},[591,1985,593],{},[588,1987,1988,1990],{},[598,1989,718],{},[720,1991,722],{},[598,1993,600],{},[588,1995,1996,1998,2038],{},[598,1997,832],{"fence":613},[1936,1999,2000,2020],{"rowspacing":1938,"columnalign":1939,"columnspacing":1940},[1942,2001,2002,2009],{},[1945,2003,2004],{},[1948,2005,2006],{"scriptlevel":1950,"displaystyle":831},[720,2007,2008],{},"101",[1945,2010,2011],{},[1948,2012,2013],{"scriptlevel":1950,"displaystyle":831},[588,2014,2015,2017],{},[598,2016,718],{},[720,2018,2019],{},"100",[1942,2021,2022,2032],{},[1945,2023,2024],{},[1948,2025,2026],{"scriptlevel":1950,"displaystyle":831},[588,2027,2028,2030],{},[598,2029,718],{},[720,2031,2019],{},[1945,2033,2034],{},[1948,2035,2036],{"scriptlevel":1950,"displaystyle":831},[720,2037,2019],{},[598,2039,837],{"fence":613},[605,2041,2042],{"encoding":607},"A = \\begin{pmatrix} 1 & 1 \\\\ 1 & 1{,}01 \\end{pmatrix}, \\qquad A^{-1} = \\begin{pmatrix} 101 & -100 \\\\ -100 & 100 \\end{pmatrix}",[572,2044,2046,2064,2269],{"className":2045,"ariaHidden":613},[612],[572,2047,2049,2052,2055,2058,2061],{"className":2048},[617],[572,2050],{"className":2051,"style":622},[621],[572,2053,593],{"className":2054},[626,627],[572,2056],{"className":2057,"style":635},[634],[572,2059,600],{"className":2060},[639],[572,2062],{"className":2063,"style":635},[634],[572,2065,2067,2071,2210,2213,2216,2220,2223,2260,2263,2266],{"className":2066},[617],[572,2068],{"className":2069,"style":2070},[621],"height:2.4em;vertical-align:-0.95em;",[572,2072,2075,2084,2204],{"className":2073},[2074],"minner",[572,2076,2080],{"className":2077,"style":2079},[857,2078],"delimcenter","top:0em;",[572,2081,832],{"className":2082},[2083,796],"delimsizing",[572,2085,2087],{"className":2086},[626],[572,2088,2090,2140,2145,2148],{"className":2089},[1936],[572,2091,2094],{"className":2092},[2093],"col-align-c",[572,2095,2097,2131],{"className":2096},[774,1217],[572,2098,2100,2128],{"className":2099},[778],[572,2101,2104,2116],{"className":2102,"style":2103},[782],"height:1.45em;",[572,2105,2107,2110],{"style":2106},"top:-3.61em;",[572,2108],{"className":2109,"style":1728},[789],[572,2111,2113],{"className":2112},[626],[572,2114,722],{"className":2115},[626],[572,2117,2119,2122],{"style":2118},"top:-2.41em;",[572,2120],{"className":2121,"style":1728},[789],[572,2123,2125],{"className":2124},[626],[572,2126,722],{"className":2127},[626],[572,2129,1244],{"className":2130},[1243],[572,2132,2134],{"className":2133},[778],[572,2135,2138],{"className":2136,"style":2137},[782],"height:0.95em;",[572,2139],{},[572,2141],{"className":2142,"style":2144},[2143],"arraycolsep","width:0.5em;",[572,2146],{"className":2147,"style":2144},[2143],[572,2149,2151],{"className":2150},[2093],[572,2152,2154,2196],{"className":2153},[774,1217],[572,2155,2157,2193],{"className":2156},[778],[572,2158,2160,2171],{"className":2159,"style":2103},[782],[572,2161,2162,2165],{"style":2106},[572,2163],{"className":2164,"style":1728},[789],[572,2166,2168],{"className":2167},[626],[572,2169,722],{"className":2170},[626],[572,2172,2173,2176],{"style":2118},[572,2174],{"className":2175,"style":1728},[789],[572,2177,2179,2182,2189],{"className":2178},[626],[572,2180,722],{"className":2181},[626],[572,2183,2185],{"className":2184},[626],[572,2186,1978],{"className":2187},[2188],"mpunct",[572,2190,2192],{"className":2191},[626],"01",[572,2194,1244],{"className":2195},[1243],[572,2197,2199],{"className":2198},[778],[572,2200,2202],{"className":2201,"style":2137},[782],[572,2203],{},[572,2205,2207],{"className":2206,"style":2079},[864,2078],[572,2208,837],{"className":2209},[2083,796],[572,2211],{"className":2212,"style":1257},[634],[572,2214,1978],{"className":2215},[2188],[572,2217],{"className":2218,"style":2219},[634],"margin-right:2em;",[572,2221],{"className":2222,"style":1257},[634],[572,2224,2226,2229],{"className":2225},[626],[572,2227,593],{"className":2228},[626,627],[572,2230,2232],{"className":2231},[770],[572,2233,2235],{"className":2234},[774],[572,2236,2238],{"className":2237},[778],[572,2239,2242],{"className":2240,"style":2241},[782],"height:0.8641em;",[572,2243,2245,2248],{"style":2244},"top:-3.113em;margin-right:0.05em;",[572,2246],{"className":2247,"style":790},[789],[572,2249,2251],{"className":2250},[794,795,796,797],[572,2252,2254,2257],{"className":2253},[626,797],[572,2255,718],{"className":2256},[626,797],[572,2258,722],{"className":2259},[626,797],[572,2261],{"className":2262,"style":635},[634],[572,2264,600],{"className":2265},[639],[572,2267],{"className":2268,"style":635},[634],[572,2270,2272,2275],{"className":2271},[617],[572,2273],{"className":2274,"style":2070},[621],[572,2276,2278,2284,2392],{"className":2277},[2074],[572,2279,2281],{"className":2280,"style":2079},[857,2078],[572,2282,832],{"className":2283},[2083,796],[572,2285,2287],{"className":2286},[626],[572,2288,2290,2338,2341,2344],{"className":2289},[1936],[572,2291,2293],{"className":2292},[2093],[572,2294,2296,2330],{"className":2295},[774,1217],[572,2297,2299,2327],{"className":2298},[778],[572,2300,2302,2313],{"className":2301,"style":2103},[782],[572,2303,2304,2307],{"style":2106},[572,2305],{"className":2306,"style":1728},[789],[572,2308,2310],{"className":2309},[626],[572,2311,2008],{"className":2312},[626],[572,2314,2315,2318],{"style":2118},[572,2316],{"className":2317,"style":1728},[789],[572,2319,2321,2324],{"className":2320},[626],[572,2322,718],{"className":2323},[626],[572,2325,2019],{"className":2326},[626],[572,2328,1244],{"className":2329},[1243],[572,2331,2333],{"className":2332},[778],[572,2334,2336],{"className":2335,"style":2137},[782],[572,2337],{},[572,2339],{"className":2340,"style":2144},[2143],[572,2342],{"className":2343,"style":2144},[2143],[572,2345,2347],{"className":2346},[2093],[572,2348,2350,2384],{"className":2349},[774,1217],[572,2351,2353,2381],{"className":2352},[778],[572,2354,2356,2370],{"className":2355,"style":2103},[782],[572,2357,2358,2361],{"style":2106},[572,2359],{"className":2360,"style":1728},[789],[572,2362,2364,2367],{"className":2363},[626],[572,2365,718],{"className":2366},[626],[572,2368,2019],{"className":2369},[626],[572,2371,2372,2375],{"style":2118},[572,2373],{"className":2374,"style":1728},[789],[572,2376,2378],{"className":2377},[626],[572,2379,2019],{"className":2380},[626],[572,2382,1244],{"className":2383},[1243],[572,2385,2387],{"className":2386},[778],[572,2388,2390],{"className":2389,"style":2137},[782],[572,2391],{},[572,2393,2395],{"className":2394,"style":2079},[864,2078],[572,2396,837],{"className":2397},[2083,796],[564,2399,2400,2401,2514,2515,2659],{},"In der Zeilensummennorm ist ",[572,2402,2404,2431],{"className":2403},[575],[572,2405,2407],{"className":2406},[579],[581,2408,2409],{"xmlns":583},[585,2410,2411,2428],{},[588,2412,2413,2415,2417,2423,2425],{},[591,2414,1292],{"mathvariant":668},[591,2416,593],{},[1166,2418,2419,2421],{},[591,2420,1292],{"mathvariant":668},[591,2422,1301],{"mathvariant":668},[598,2424,600],{},[720,2426,2427],{},"2,01",[605,2429,2430],{"encoding":607},"\\|A\\|_\\infty = 2{,}01",[572,2432,2434,2495],{"className":2433,"ariaHidden":613},[612],[572,2435,2437,2440,2443,2446,2486,2489,2492],{"className":2436},[617],[572,2438],{"className":2439,"style":850},[621],[572,2441,1292],{"className":2442},[626],[572,2444,593],{"className":2445},[626,627],[572,2447,2449,2452],{"className":2448},[626],[572,2450,1292],{"className":2451},[626],[572,2453,2455],{"className":2454},[770],[572,2456,2458,2478],{"className":2457},[774,1217],[572,2459,2461,2475],{"className":2460},[778],[572,2462,2464],{"className":2463,"style":1376},[782],[572,2465,2466,2469],{"style":1379},[572,2467],{"className":2468,"style":790},[789],[572,2470,2472],{"className":2471},[794,795,796,797],[572,2473,1301],{"className":2474},[626,797],[572,2476,1244],{"className":2477},[1243],[572,2479,2481],{"className":2480},[778],[572,2482,2484],{"className":2483,"style":1398},[782],[572,2485],{},[572,2487],{"className":2488,"style":635},[634],[572,2490,600],{"className":2491},[639],[572,2493],{"className":2494,"style":635},[634],[572,2496,2498,2502,2505,2511],{"className":2497},[617],[572,2499],{"className":2500,"style":2501},[621],"height:0.8389em;vertical-align:-0.1944em;",[572,2503,1582],{"className":2504},[626],[572,2506,2508],{"className":2507},[626],[572,2509,1978],{"className":2510},[2188],[572,2512,2192],{"className":2513},[626]," und ",[572,2516,2518,2553],{"className":2517},[575],[572,2519,2521],{"className":2520},[579],[581,2522,2523],{"xmlns":583},[585,2524,2525,2550],{},[588,2526,2527,2529,2539,2545,2547],{},[591,2528,1292],{"mathvariant":668},[710,2530,2531,2533],{},[591,2532,593],{},[588,2534,2535,2537],{},[598,2536,718],{},[720,2538,722],{},[1166,2540,2541,2543],{},[591,2542,1292],{"mathvariant":668},[591,2544,1301],{"mathvariant":668},[598,2546,600],{},[720,2548,2549],{},"201",[605,2551,2552],{"encoding":607},"\\|A^{-1}\\|_\\infty = 201",[572,2554,2556,2650],{"className":2555,"ariaHidden":613},[612],[572,2557,2559,2563,2566,2601,2641,2644,2647],{"className":2558},[617],[572,2560],{"className":2561,"style":2562},[621],"height:1.0641em;vertical-align:-0.25em;",[572,2564,1292],{"className":2565},[626],[572,2567,2569,2572],{"className":2568},[626],[572,2570,593],{"className":2571},[626,627],[572,2573,2575],{"className":2574},[770],[572,2576,2578],{"className":2577},[774],[572,2579,2581],{"className":2580},[778],[572,2582,2584],{"className":2583,"style":760},[782],[572,2585,2586,2589],{"style":785},[572,2587],{"className":2588,"style":790},[789],[572,2590,2592],{"className":2591},[794,795,796,797],[572,2593,2595,2598],{"className":2594},[626,797],[572,2596,718],{"className":2597},[626,797],[572,2599,722],{"className":2600},[626,797],[572,2602,2604,2607],{"className":2603},[626],[572,2605,1292],{"className":2606},[626],[572,2608,2610],{"className":2609},[770],[572,2611,2613,2633],{"className":2612},[774,1217],[572,2614,2616,2630],{"className":2615},[778],[572,2617,2619],{"className":2618,"style":1376},[782],[572,2620,2621,2624],{"style":1379},[572,2622],{"className":2623,"style":790},[789],[572,2625,2627],{"className":2626},[794,795,796,797],[572,2628,1301],{"className":2629},[626,797],[572,2631,1244],{"className":2632},[1243],[572,2634,2636],{"className":2635},[778],[572,2637,2639],{"className":2638,"style":1398},[782],[572,2640],{},[572,2642],{"className":2643,"style":635},[634],[572,2645,600],{"className":2646},[639],[572,2648],{"className":2649,"style":635},[634],[572,2651,2653,2656],{"className":2652},[617],[572,2654],{"className":2655,"style":966},[621],[572,2657,2549],{"className":2658},[626],", also",[572,2661,2663],{"className":2662},[1913],[572,2664,2666,2704],{"className":2665},[575],[572,2667,2669],{"className":2668},[579],[581,2670,2671],{"xmlns":583,"display":1922},[585,2672,2673,2701],{},[588,2674,2675,2681,2683,2685,2687,2689,2691,2694,2696,2698],{},[1166,2676,2677,2679],{},[591,2678,828],{},[591,2680,1301],{"mathvariant":668},[598,2682,832],{"stretchy":831},[591,2684,593],{},[598,2686,837],{"stretchy":831},[598,2688,600],{},[720,2690,2427],{},[598,2692,2693],{},"⋅",[720,2695,2549],{},[598,2697,600],{},[720,2699,2700],{},"404,01",[605,2702,2703],{"encoding":607},"\\kappa_\\infty(A) = 2{,}01 \\cdot 201 = 404{,}01",[572,2705,2707,2771,2800,2818],{"className":2706,"ariaHidden":613},[612],[572,2708,2710,2713,2753,2756,2759,2762,2765,2768],{"className":2709},[617],[572,2711],{"className":2712,"style":850},[621],[572,2714,2716,2719],{"className":2715},[626],[572,2717,828],{"className":2718},[626,627],[572,2720,2722],{"className":2721},[770],[572,2723,2725,2745],{"className":2724},[774,1217],[572,2726,2728,2742],{"className":2727},[778],[572,2729,2731],{"className":2730,"style":1376},[782],[572,2732,2733,2736],{"style":1379},[572,2734],{"className":2735,"style":790},[789],[572,2737,2739],{"className":2738},[794,795,796,797],[572,2740,1301],{"className":2741},[626,797],[572,2743,1244],{"className":2744},[1243],[572,2746,2748],{"className":2747},[778],[572,2749,2751],{"className":2750,"style":1398},[782],[572,2752],{},[572,2754,832],{"className":2755},[857],[572,2757,593],{"className":2758},[626,627],[572,2760,837],{"className":2761},[864],[572,2763],{"className":2764,"style":635},[634],[572,2766,600],{"className":2767},[639],[572,2769],{"className":2770,"style":635},[634],[572,2772,2774,2777,2780,2786,2789,2793,2797],{"className":2773},[617],[572,2775],{"className":2776,"style":2501},[621],[572,2778,1582],{"className":2779},[626],[572,2781,2783],{"className":2782},[626],[572,2784,1978],{"className":2785},[2188],[572,2787,2192],{"className":2788},[626],[572,2790],{"className":2791,"style":2792},[634],"margin-right:0.2222em;",[572,2794,2693],{"className":2795},[2796],"mbin",[572,2798],{"className":2799,"style":2792},[634],[572,2801,2803,2806,2809,2812,2815],{"className":2802},[617],[572,2804],{"className":2805,"style":966},[621],[572,2807,2549],{"className":2808},[626],[572,2810],{"className":2811,"style":635},[634],[572,2813,600],{"className":2814},[639],[572,2816],{"className":2817,"style":635},[634],[572,2819,2821,2824,2828,2834],{"className":2820},[617],[572,2822],{"className":2823,"style":2501},[621],[572,2825,2827],{"className":2826},[626],"404",[572,2829,2831],{"className":2830},[626],[572,2832,1978],{"className":2833},[2188],[572,2835,2192],{"className":2836},[626],[564,2838,2839,2840,2931,2932,3011,3012,3052,3053,3110,3111,3266,3267,3404,3405,3433,3434,3472,3473,3594],{},"Zu ",[572,2841,2843,2874],{"className":2842},[575],[572,2844,2846],{"className":2845},[579],[581,2847,2848],{"xmlns":583},[585,2849,2850,2871],{},[588,2851,2852,2854,2856,2858,2860,2863,2867,2869],{},[591,2853,603],{},[598,2855,600],{},[598,2857,832],{"stretchy":831},[720,2859,1582],{},[598,2861,2862],{"separator":613},";",[2864,2865,2866],"mtext",{}," ",[720,2868,2427],{},[598,2870,837],{"stretchy":831},[605,2872,2873],{"encoding":607},"b = (2;\\ 2{,}01)",[572,2875,2877,2895],{"className":2876,"ariaHidden":613},[612],[572,2878,2880,2883,2886,2889,2892],{"className":2879},[617],[572,2881],{"className":2882,"style":649},[621],[572,2884,603],{"className":2885},[626,627],[572,2887],{"className":2888,"style":635},[634],[572,2890,600],{"className":2891},[639],[572,2893],{"className":2894,"style":635},[634],[572,2896,2898,2901,2904,2907,2910,2913,2916,2919,2925,2928],{"className":2897},[617],[572,2899],{"className":2900,"style":850},[621],[572,2902,832],{"className":2903},[857],[572,2905,1582],{"className":2906},[626],[572,2908,2862],{"className":2909},[2188],[572,2911,2866],{"className":2912},[634],[572,2914],{"className":2915,"style":1257},[634],[572,2917,1582],{"className":2918},[626],[572,2920,2922],{"className":2921},[626],[572,2923,1978],{"className":2924},[2188],[572,2926,2192],{"className":2927},[626],[572,2929,837],{"className":2930},[864]," gehört die Lösung ",[572,2933,2935,2963],{"className":2934},[575],[572,2936,2938],{"className":2937},[579],[581,2939,2940],{"xmlns":583},[585,2941,2942,2960],{},[588,2943,2944,2946,2948,2950,2952,2954,2956,2958],{},[591,2945,596],{},[598,2947,600],{},[598,2949,832],{"stretchy":831},[720,2951,722],{},[598,2953,2862],{"separator":613},[2864,2955,2866],{},[720,2957,722],{},[598,2959,837],{"stretchy":831},[605,2961,2962],{"encoding":607},"x = (1;\\ 1)",[572,2964,2966,2984],{"className":2965,"ariaHidden":613},[612],[572,2967,2969,2972,2975,2978,2981],{"className":2968},[617],[572,2970],{"className":2971,"style":1079},[621],[572,2973,596],{"className":2974},[626,627],[572,2976],{"className":2977,"style":635},[634],[572,2979,600],{"className":2980},[639],[572,2982],{"className":2983,"style":635},[634],[572,2985,2987,2990,2993,2996,2999,3002,3005,3008],{"className":2986},[617],[572,2988],{"className":2989,"style":850},[621],[572,2991,832],{"className":2992},[857],[572,2994,722],{"className":2995},[626],[572,2997,2862],{"className":2998},[2188],[572,3000,2866],{"className":3001},[634],[572,3003],{"className":3004,"style":1257},[634],[572,3006,722],{"className":3007},[626],[572,3009,837],{"className":3010},[864],". Ändert man nur die zweite Komponente auf ",[572,3013,3015,3030],{"className":3014},[575],[572,3016,3018],{"className":3017},[579],[581,3019,3020],{"xmlns":583},[585,3021,3022,3027],{},[588,3023,3024],{},[720,3025,3026],{},"2,02",[605,3028,3029],{"encoding":607},"2{,}02",[572,3031,3033],{"className":3032,"ariaHidden":613},[612],[572,3034,3036,3039,3042,3048],{"className":3035},[617],[572,3037],{"className":3038,"style":2501},[621],[572,3040,1582],{"className":3041},[626],[572,3043,3045],{"className":3044},[626],[572,3046,1978],{"className":3047},[2188],[572,3049,3051],{"className":3050},[626],"02",", ist die Lösung ",[572,3054,3056,3080],{"className":3055},[575],[572,3057,3059],{"className":3058},[579],[581,3060,3061],{"xmlns":583},[585,3062,3063,3077],{},[588,3064,3065,3067,3069,3071,3073,3075],{},[598,3066,832],{"stretchy":831},[720,3068,1950],{},[598,3070,2862],{"separator":613},[2864,3072,2866],{},[720,3074,1582],{},[598,3076,837],{"stretchy":831},[605,3078,3079],{"encoding":607},"(0;\\ 2)",[572,3081,3083],{"className":3082,"ariaHidden":613},[612],[572,3084,3086,3089,3092,3095,3098,3101,3104,3107],{"className":3085},[617],[572,3087],{"className":3088,"style":850},[621],[572,3090,832],{"className":3091},[857],[572,3093,1950],{"className":3094},[626],[572,3096,2862],{"className":3097},[2188],[572,3099,2866],{"className":3100},[634],[572,3102],{"className":3103,"style":1257},[634],[572,3105,1582],{"className":3106},[626],[572,3108,837],{"className":3109},[864],". Die rechte Seite ändert sich relativ um ",[572,3112,3114,3139],{"className":3113},[575],[572,3115,3117],{"className":3116},[579],[581,3118,3119],{"xmlns":583},[585,3120,3121,3136],{},[588,3122,3123,3130,3133],{},[1592,3124,3125,3128],{},[720,3126,3127],{},"0,01",[720,3129,2427],{},[598,3131,3132],{},"≈",[720,3134,3135],{},"0,005",[605,3137,3138],{"encoding":607},"\\frac{0{,}01}{2{,}01} \\approx 0{,}005",[572,3140,3142,3247],{"className":3141,"ariaHidden":613},[612],[572,3143,3145,3149,3238,3241,3244],{"className":3144},[617],[572,3146],{"className":3147,"style":3148},[621],"height:1.3783em;vertical-align:-0.4811em;",[572,3150,3152,3155,3235],{"className":3151},[626],[572,3153],{"className":3154},[857,1708],[572,3156,3158],{"className":3157},[1592],[572,3159,3161,3226],{"className":3160},[774,1217],[572,3162,3164,3223],{"className":3163},[778],[572,3165,3168,3191,3199],{"className":3166,"style":3167},[782],"height:0.8972em;",[572,3169,3170,3173],{"style":1724},[572,3171],{"className":3172,"style":1728},[789],[572,3174,3176],{"className":3175},[794,795,796,797],[572,3177,3179,3182,3188],{"className":3178},[626,797],[572,3180,1582],{"className":3181},[626,797],[572,3183,3185],{"className":3184},[626,797],[572,3186,1978],{"className":3187},[2188,797],[572,3189,2192],{"className":3190},[626,797],[572,3192,3193,3196],{"style":1803},[572,3194],{"className":3195,"style":1728},[789],[572,3197],{"className":3198,"style":1811},[1810],[572,3200,3202,3205],{"style":3201},"top:-3.4461em;",[572,3203],{"className":3204,"style":1728},[789],[572,3206,3208],{"className":3207},[794,795,796,797],[572,3209,3211,3214,3220],{"className":3210},[626,797],[572,3212,1950],{"className":3213},[626,797],[572,3215,3217],{"className":3216},[626,797],[572,3218,1978],{"className":3219},[2188,797],[572,3221,2192],{"className":3222},[626,797],[572,3224,1244],{"className":3225},[1243],[572,3227,3229],{"className":3228},[778],[572,3230,3233],{"className":3231,"style":3232},[782],"height:0.4811em;",[572,3234],{},[572,3236],{"className":3237},[864,1708],[572,3239],{"className":3240,"style":635},[634],[572,3242,3132],{"className":3243},[639],[572,3245],{"className":3246,"style":635},[634],[572,3248,3250,3253,3256,3262],{"className":3249},[617],[572,3251],{"className":3252,"style":2501},[621],[572,3254,1950],{"className":3255},[626],[572,3257,3259],{"className":3258},[626],[572,3260,1978],{"className":3261},[2188],[572,3263,3265],{"className":3264},[626],"005",", also ein halbes Prozent. Die Lösung ändert sich relativ um ",[572,3268,3270,3298],{"className":3269},[575],[572,3271,3273],{"className":3272},[579],[581,3274,3275],{"xmlns":583},[585,3276,3277,3295],{},[588,3278,3279,3285,3287,3289,3292],{},[1592,3280,3281,3283],{},[720,3282,722],{},[720,3284,722],{},[598,3286,600],{},[720,3288,2019],{},[2864,3290,3291],{}," ",[591,3293,3294],{"mathvariant":668},"%",[605,3296,3297],{"encoding":607},"\\frac{1}{1} = 100\\,\\%",[572,3299,3301,3388],{"className":3300,"ariaHidden":613},[612],[572,3302,3304,3308,3379,3382,3385],{"className":3303},[617],[572,3305],{"className":3306,"style":3307},[621],"height:1.1901em;vertical-align:-0.345em;",[572,3309,3311,3314,3376],{"className":3310},[626],[572,3312],{"className":3313},[857,1708],[572,3315,3317],{"className":3316},[1592],[572,3318,3320,3367],{"className":3319},[774,1217],[572,3321,3323,3364],{"className":3322},[778],[572,3324,3327,3341,3349],{"className":3325,"style":3326},[782],"height:0.8451em;",[572,3328,3329,3332],{"style":1724},[572,3330],{"className":3331,"style":1728},[789],[572,3333,3335],{"className":3334},[794,795,796,797],[572,3336,3338],{"className":3337},[626,797],[572,3339,722],{"className":3340},[626,797],[572,3342,3343,3346],{"style":1803},[572,3344],{"className":3345,"style":1728},[789],[572,3347],{"className":3348,"style":1811},[1810],[572,3350,3352,3355],{"style":3351},"top:-3.394em;",[572,3353],{"className":3354,"style":1728},[789],[572,3356,3358],{"className":3357},[794,795,796,797],[572,3359,3361],{"className":3360},[626,797],[572,3362,722],{"className":3363},[626,797],[572,3365,1244],{"className":3366},[1243],[572,3368,3370],{"className":3369},[778],[572,3371,3374],{"className":3372,"style":3373},[782],"height:0.345em;",[572,3375],{},[572,3377],{"className":3378},[864,1708],[572,3380],{"className":3381,"style":635},[634],[572,3383,600],{"className":3384},[639],[572,3386],{"className":3387,"style":635},[634],[572,3389,3391,3395,3398,3401],{"className":3390},[617],[572,3392],{"className":3393,"style":3394},[621],"height:0.8056em;vertical-align:-0.0556em;",[572,3396,2019],{"className":3397},[626],[572,3399],{"className":3400,"style":1257},[634],[572,3402,3294],{"className":3403},[626],". Der Verstärkungsfaktor ",[572,3406,3408,3421],{"className":3407},[575],[572,3409,3411],{"className":3410},[579],[581,3412,3413],{"xmlns":583},[585,3414,3415,3419],{},[588,3416,3417],{},[720,3418,2549],{},[605,3420,2549],{"encoding":607},[572,3422,3424],{"className":3423,"ariaHidden":613},[612],[572,3425,3427,3430],{"className":3426},[617],[572,3428],{"className":3429,"style":966},[621],[572,3431,2549],{"className":3432},[626]," liegt unter der Schranke ",[572,3435,3437,3451],{"className":3436},[575],[572,3438,3440],{"className":3439},[579],[581,3441,3442],{"xmlns":583},[585,3443,3444,3448],{},[588,3445,3446],{},[720,3447,2700],{},[605,3449,3450],{"encoding":607},"404{,}01",[572,3452,3454],{"className":3453,"ariaHidden":613},[612],[572,3455,3457,3460,3463,3469],{"className":3456},[617],[572,3458],{"className":3459,"style":2501},[621],[572,3461,2827],{"className":3462},[626],[572,3464,3466],{"className":3465},[626],[572,3467,1978],{"className":3468},[2188],[572,3470,2192],{"className":3471},[626],". Nach der Faustregel gehen hier etwa ",[572,3474,3476,3505],{"className":3475},[575],[572,3477,3479],{"className":3478},[579],[581,3480,3481],{"xmlns":583},[585,3482,3483,3502],{},[588,3484,3485,3495,3497,3499],{},[1166,3486,3487,3493],{},[588,3488,3489,3491],{},[591,3490,1172],{},[598,3492,1175],{},[720,3494,1178],{},[720,3496,2827],{},[598,3498,3132],{},[720,3500,3501],{},"2,6",[605,3503,3504],{"encoding":607},"\\log_{10} 404 \\approx 2{,}6",[572,3506,3508,3575],{"className":3507,"ariaHidden":613},[612],[572,3509,3511,3515,3560,3563,3566,3569,3572],{"className":3510},[617],[572,3512],{"className":3513,"style":3514},[621],"height:0.9386em;vertical-align:-0.2441em;",[572,3516,3518,3523],{"className":3517},[1202],[572,3519,1206,3521],{"className":3520},[1202],[572,3522,1210],{"style":1209},[572,3524,3526],{"className":3525},[770],[572,3527,3529,3552],{"className":3528},[774,1217],[572,3530,3532,3549],{"className":3531},[778],[572,3533,3535],{"className":3534,"style":1224},[782],[572,3536,3537,3540],{"style":1227},[572,3538],{"className":3539,"style":790},[789],[572,3541,3543],{"className":3542},[794,795,796,797],[572,3544,3546],{"className":3545},[626,797],[572,3547,1178],{"className":3548},[626,797],[572,3550,1244],{"className":3551},[1243],[572,3553,3555],{"className":3554},[778],[572,3556,3558],{"className":3557,"style":1251},[782],[572,3559],{},[572,3561],{"className":3562,"style":1257},[634],[572,3564,2827],{"className":3565},[626],[572,3567],{"className":3568,"style":635},[634],[572,3570,3132],{"className":3571},[639],[572,3573],{"className":3574,"style":635},[634],[572,3576,3578,3581,3584,3590],{"className":3577},[617],[572,3579],{"className":3580,"style":2501},[621],[572,3582,1582],{"className":3583},[626],[572,3585,3587],{"className":3586},[626],[572,3588,1978],{"className":3589},[2188],[572,3591,3593],{"className":3592},[626],"6"," Stellen verloren.",[559,3596,3598],{"id":3597},"typische-fehler","Typische Fehler",[896,3600,3601,3810,3932,3935],{},[899,3602,3603,3604,3667,3668,3706,3707,3758,3759,3809],{},"Eine kleine Determinante mit schlechter Kondition gleichsetzen. ",[572,3605,3607,3627],{"className":3606},[575],[572,3608,3610],{"className":3609},[579],[581,3611,3612],{"xmlns":583},[585,3613,3614,3624],{},[588,3615,3616,3619,3621],{},[720,3617,3618],{},"0,1",[598,3620,2693],{},[591,3622,3623],{},"I",[605,3625,3626],{"encoding":607},"0{,}1 \\cdot I",[572,3628,3630,3657],{"className":3629,"ariaHidden":613},[612],[572,3631,3633,3636,3639,3645,3648,3651,3654],{"className":3632},[617],[572,3634],{"className":3635,"style":2501},[621],[572,3637,1950],{"className":3638},[626],[572,3640,3642],{"className":3641},[626],[572,3643,1978],{"className":3644},[2188],[572,3646,722],{"className":3647},[626],[572,3649],{"className":3650,"style":2792},[634],[572,3652,2693],{"className":3653},[2796],[572,3655],{"className":3656,"style":2792},[634],[572,3658,3660,3663],{"className":3659},[617],[572,3661],{"className":3662,"style":622},[621],[572,3664,3623],{"className":3665,"style":3666},[626,627],"margin-right:0.0785em;"," hat die Determinante ",[572,3669,3671,3685],{"className":3670},[575],[572,3672,3674],{"className":3673},[579],[581,3675,3676],{"xmlns":583},[585,3677,3678,3682],{},[588,3679,3680],{},[720,3681,3127],{},[605,3683,3684],{"encoding":607},"0{,}01",[572,3686,3688],{"className":3687,"ariaHidden":613},[612],[572,3689,3691,3694,3697,3703],{"className":3690},[617],[572,3692],{"className":3693,"style":2501},[621],[572,3695,1950],{"className":3696},[626],[572,3698,3700],{"className":3699},[626],[572,3701,1978],{"className":3702},[2188],[572,3704,2192],{"className":3705},[626]," (bei ",[572,3708,3710,3728],{"className":3709},[575],[572,3711,3713],{"className":3712},[579],[581,3714,3715],{"xmlns":583},[585,3716,3717,3725],{},[588,3718,3719,3721,3723],{},[591,3720,1785],{},[598,3722,600],{},[720,3724,1582],{},[605,3726,3727],{"encoding":607},"n = 2",[572,3729,3731,3749],{"className":3730,"ariaHidden":613},[612],[572,3732,3734,3737,3740,3743,3746],{"className":3733},[617],[572,3735],{"className":3736,"style":1079},[621],[572,3738,1785],{"className":3739},[626,627],[572,3741],{"className":3742,"style":635},[634],[572,3744,600],{"className":3745},[639],[572,3747],{"className":3748,"style":635},[634],[572,3750,3752,3755],{"className":3751},[617],[572,3753],{"className":3754,"style":966},[621],[572,3756,1582],{"className":3757},[626],"), ist aber mit ",[572,3760,3762,3779],{"className":3761},[575],[572,3763,3765],{"className":3764},[579],[581,3766,3767],{"xmlns":583},[585,3768,3769,3777],{},[588,3770,3771,3773,3775],{},[591,3772,828],{},[598,3774,600],{},[720,3776,722],{},[605,3778,1069],{"encoding":607},[572,3780,3782,3800],{"className":3781,"ariaHidden":613},[612],[572,3783,3785,3788,3791,3794,3797],{"className":3784},[617],[572,3786],{"className":3787,"style":1079},[621],[572,3789,828],{"className":3790},[626,627],[572,3792],{"className":3793,"style":635},[634],[572,3795,600],{"className":3796},[639],[572,3798],{"className":3799,"style":635},[634],[572,3801,3803,3806],{"className":3802},[617],[572,3804],{"className":3805,"style":966},[621],[572,3807,722],{"className":3808},[626]," perfekt konditioniert.",[899,3811,3812,3813,2514,3852,3931],{},"Normen mischen: ",[572,3814,3816,3834],{"className":3815},[575],[572,3817,3819],{"className":3818},[579],[581,3820,3821],{"xmlns":583},[585,3822,3823,3831],{},[588,3824,3825,3827,3829],{},[591,3826,1292],{"mathvariant":668},[591,3828,593],{},[591,3830,1292],{"mathvariant":668},[605,3832,3833],{"encoding":607},"\\|A\\|",[572,3835,3837],{"className":3836,"ariaHidden":613},[612],[572,3838,3840,3843,3846,3849],{"className":3839},[617],[572,3841],{"className":3842,"style":850},[621],[572,3844,1292],{"className":3845},[626],[572,3847,593],{"className":3848},[626,627],[572,3850,1292],{"className":3851},[626],[572,3853,3855,3881],{"className":3854},[575],[572,3856,3858],{"className":3857},[579],[581,3859,3860],{"xmlns":583},[585,3861,3862,3878],{},[588,3863,3864,3866,3876],{},[591,3865,1292],{"mathvariant":668},[710,3867,3868,3870],{},[591,3869,593],{},[588,3871,3872,3874],{},[598,3873,718],{},[720,3875,722],{},[591,3877,1292],{"mathvariant":668},[605,3879,3880],{"encoding":607},"\\|A^{-1}\\|",[572,3882,3884],{"className":3883,"ariaHidden":613},[612],[572,3885,3887,3890,3893,3928],{"className":3886},[617],[572,3888],{"className":3889,"style":2562},[621],[572,3891,1292],{"className":3892},[626],[572,3894,3896,3899],{"className":3895},[626],[572,3897,593],{"className":3898},[626,627],[572,3900,3902],{"className":3901},[770],[572,3903,3905],{"className":3904},[774],[572,3906,3908],{"className":3907},[778],[572,3909,3911],{"className":3910,"style":760},[782],[572,3912,3913,3916],{"style":785},[572,3914],{"className":3915,"style":790},[789],[572,3917,3919],{"className":3918},[794,795,796,797],[572,3920,3922,3925],{"className":3921},[626,797],[572,3923,718],{"className":3924},[626,797],[572,3926,722],{"className":3927},[626,797],[572,3929,1292],{"className":3930},[626]," müssen in derselben Norm berechnet werden.",[899,3933,3934],{},"Die Ungleichung als Gleichung lesen. Sie gibt den schlimmsten Fall an; oft ist die tatsächliche Verstärkung kleiner.",[899,3936,3937],{},"Bei schlechter Kondition die Schuld beim Verfahren suchen. Auch exakte Rechnung reagiert so stark auf gestörte Daten.",{"title":3939,"searchDepth":3940,"depth":3940,"links":3941},"",2,[3942,3943,3944],{"id":561,"depth":3940,"text":562},{"id":1908,"depth":3940,"text":1909},{"id":3597,"depth":3940,"text":3598},[3946,3949,3951,3954,3956,3959,3961,3964,3966,3969,3972,3974],{"lhs":3947,"rhs":3948},"det([[1, 1], [1, 1.01]])","0.01",{"lhs":3950,"rhs":2008},"inv([[1, 1], [1, 1.01]])[1, 1]",{"lhs":3952,"rhs":3953},"inv([[1, 1], [1, 1.01]])[1, 2]","-100",{"lhs":3955,"rhs":2019},"inv([[1, 1], [1, 1.01]])[2, 2]",{"lhs":3957,"rhs":3958},"1 + 1.01","2.01",{"lhs":3960,"rhs":2549},"101 + 100",{"lhs":3962,"rhs":3963},"2.01*201","404.01",{"lhs":3965,"rhs":3958},"1*1 + 1.01*1",{"lhs":3967,"rhs":3968},"1*0 + 1.01*2","2.02",{"lhs":3970,"rhs":3971},"round(0.01\u002F2.01, 4)","0.005",{"lhs":3973,"rhs":2549},"(1\u002F1)\u002F(0.01\u002F2.01)",{"lhs":3975,"rhs":3976},"round(log10(404.01), 1)","2.6","A \\text{ invertierbar},\\ A x = b,\\ A(x + \\Delta x) = b + \\Delta b,\\ b \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">invertierbar\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A x = b,\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A(x + \\Delta x) = b + \\Delta b,\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=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:0.7778em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b \\neq 0\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","condition-number","\\kappa(A) = \\|A\\| \\cdot \\|A^{-1}\\|, \\qquad \\frac{\\|\\Delta x\\|}{\\|x\\|} \\leq \\kappa(A)\\,\\frac{\\|\\Delta b\\|}{\\|b\\|}","\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>\u003Cmi>κ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi>κ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\kappa(A) = \\|A\\| \\cdot \\|A^{-1}\\|, \\qquad \\frac{\\|\\Delta x\\|}{\\|x\\|} \\leq \\kappa(A)\\,\\frac{\\|\\Delta b\\|}{\\|b\\|}\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=\"mord mathnormal\">κ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\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:2.363em;vertical-align:-0.936em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;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\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\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=\"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=\"mord\">∥\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\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\">∥Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\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>\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:2.363em;vertical-align:-0.936em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">κ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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=\"mord\">∥\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\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\">∥Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\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\u002Fnumerics\u002Fkonditionszahl",[],[3990,3991,3992,3993],"jacobi-method","lu-decomposition","inverse-2x2","rounding-error",{"title":548,"description":3939},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fkonditionszahl","Die Konditionszahl gibt an, wie stark sich relative Fehler in der rechten Seite höchstens auf die Lösung auswirken.",[3998,3999,4000,4001],"kondition","matrixnorm","fehleranalyse","lineares gleichungssystem",[4003,4006,4009,4013,4017],{"symbol":840,"meaning":4004,"symbolHtml":4005},"Konditionszahl der Matrix A bezüglich der gewählten Norm","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>κ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\kappa(A)\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=\"mord mathnormal\">κ\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3833,"meaning":4007,"symbolHtml":4008},"Matrixnorm von A, passend zur verwendeten Vektornorm","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∥\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\|A\\|\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=\"mord\">∥\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord\">∥\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4010,"meaning":4011,"symbolHtml":4012},"A^{-1}","inverse Matrix","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A^{-1}\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:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;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\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4014,"meaning":4015,"symbolHtml":4016},"x, \\Delta x","exakte Lösung und ihre Änderung","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x, \\Delta x\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4018,"meaning":4019,"symbolHtml":4020},"b, \\Delta b","rechte Seite und ihre Störung (z.B. Mess- oder Rundungsfehler)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b, \\Delta b\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","N0ddQANyDKKN-h7Z8WxemLeZyTaWN2tejmFZHrox7Xc",[4023,4026,4029,4032],{"stem":4024,"title":4025,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fabsoluter-und-relativer-fehler","Absoluter und relativer Fehler",{"stem":4027,"title":4028,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Finverse-2x2-matrix","Inverse einer 2×2-Matrix",{"stem":4030,"title":4031,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Fjacobi-verfahren","Jacobi-Verfahren",{"stem":4033,"title":4034,"category":391},"de\u002Fformulas\u002Fmath\u002Fnumerics\u002Flu-zerlegung","LU-Zerlegung",1793824265812]