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x",[569,1034,1036,1089],{"className":1035,"ariaHidden":630},[629],[569,1037,1039,1043,1080,1083,1086],{"className":1038},[634],[569,1040],{"className":1041,"style":1042},[638],"height:0.725em;vertical-align:-0.011em;",[569,1044,1046],{"className":1045},[643,775],[569,1047,1049],{"className":1048},[779],[569,1050,1052],{"className":1051},[783],[569,1053,1056,1064],{"className":1054,"style":1055},[787],"height:0.714em;",[569,1057,1058,1061],{"style":790},[569,1059],{"className":1060,"style":795},[794],[569,1062,1016],{"className":1063},[643,644],[569,1065,1066,1069],{"style":790},[569,1067],{"className":1068,"style":795},[794],[569,1070,1073],{"className":1071,"style":1072},[808],"left:-0.2077em;",[569,1074,1076],{"className":1075,"style":814},[813],[816,1077,1078],{"xmlns":818,"width":819,"height":820,"style":821,"viewBox":822,"preserveAspectRatio":823},[825,1079],{"d":827},[569,1081],{"className":1082,"style":684},[592],[569,1084,1021],{"className":1085},[672],[569,1087],{"className":1088,"style":684},[592],[569,1090,1092,1095,1098],{"className":1091},[634],[569,1093],{"className":1094,"style":1055},[638],[569,1096,898],{"className":1097},[643,644],[569,1099,1101],{"className":1100},[643,775],[569,1102,1104],{"className":1103},[779],[569,1105,1107],{"className":1106},[783],[569,1108,1110,1118],{"className":1109,"style":1055},[787],[569,1111,1112,1115],{"style":790},[569,1113],{"className":1114,"style":795},[794],[569,1116,1016],{"className":1117},[643,644],[569,1119,1120,1123],{"style":790},[569,1121],{"className":1122,"style":795},[794],[569,1124,1126],{"className":1125,"style":1072},[808],[569,1127,1129],{"className":1128,"style":814},[813],[816,1130,1131],{"xmlns":818,"width":819,"height":820,"style":821,"viewBox":822,"preserveAspectRatio":823},[825,1132],{"d":827}," lautet sie",[569,1135,1138],{"className":1136},[1137],"katex-display",[569,1139,1141,1189],{"className":1140},[572],[569,1142,1144],{"className":1143},[576],[578,1145,1147],{"xmlns":580,"display":1146},"block",[582,1148,1149,1186],{},[585,1150,1151,1153,1156,1158,1160,1163,1165,1167,1170,1173,1175,1179,1181,1184],{},[588,1152,919],{},[598,1154,1155],{},"=",[588,1157,851],{},[598,1159,854],{},[588,1161,735],{"mathvariant":1162},"normal",[598,1164,854],{},[588,1166,898],{},[598,1168,1169],{},"+",[588,1171,1172],{"mathvariant":1162},"rg",[598,1174,854],{},[598,1176,1178],{"stretchy":1177},"false","(",[588,1180,898],{},[598,1182,1183],{"stretchy":1177},")",[588,1185,880],{"mathvariant":1162},[622,1187,1188],{"encoding":624},"n = \\dim \\operatorname{Kern} A + \\operatorname{rg}(A).",[569,1190,1192,1211,1246],{"className":1191,"ariaHidden":630},[629],[569,1193,1195,1199,1202,1205,1208],{"className":1194},[634],[569,1196],{"className":1197,"style":1198},[638],"height:0.4306em;",[569,1200,919],{"className":1201},[643,644],[569,1203],{"className":1204,"style":684},[592],[569,1206,1155],{"className":1207},[672],[569,1209],{"className":1210,"style":684},[592],[569,1212,1214,1218,1221,1224,1231,1234,1237,1240,1243],{"className":1213},[634],[569,1215],{"className":1216,"style":1217},[638],"height:0.7778em;vertical-align:-0.0833em;",[569,1219,851],{"className":1220},[873],[569,1222],{"className":1223,"style":665},[592],[569,1225,1227],{"className":1226},[873],[569,1228,735],{"className":1229},[643,1230],"mathrm",[569,1232],{"className":1233,"style":665},[592],[569,1235,898],{"className":1236},[643,644],[569,1238],{"className":1239,"style":680},[592],[569,1241,1169],{"className":1242},[995],[569,1244],{"className":1245,"style":680},[592],[569,1247,1249,1253,1260,1264,1267,1271],{"className":1248},[634],[569,1250],{"className":1251,"style":1252},[638],"height:1em;vertical-align:-0.25em;",[569,1254,1256],{"className":1255},[873],[569,1257,1172],{"className":1258,"style":1259},[643,1230],"margin-right:0.0139em;",[569,1261,1178],{"className":1262},[1263],"mopen",[569,1265,898],{"className":1266},[643,644],[569,1268,1183],{"className":1269},[1270],"mclose",[569,1272,880],{"className":1273},[643],[565,1275,1276,1277,1305,1306,1309,1310,1404,1405,880],{},"Dabei ist ",[569,1278,1280,1293],{"className":1279},[572],[569,1281,1283],{"className":1282},[576],[578,1284,1285],{"xmlns":580},[582,1286,1287,1291],{},[585,1288,1289],{},[588,1290,919],{},[622,1292,919],{"encoding":624},[569,1294,1296],{"className":1295,"ariaHidden":630},[629],[569,1297,1299,1302],{"className":1298},[634],[569,1300],{"className":1301,"style":1198},[638],[569,1303,919],{"className":1304},[643,644]," die ",[733,1307,1308],{},"Spaltenzahl",", nicht die Zeilenzahl, und ",[569,1311,1313,1347],{"className":1312},[572],[569,1314,1316],{"className":1315},[576],[578,1317,1318],{"xmlns":580},[582,1319,1320,1344],{},[585,1321,1322,1324,1326,1328,1330,1332,1334,1336,1338,1340,1342],{},[588,1323,1172],{"mathvariant":1162},[598,1325,854],{},[598,1327,1178],{"stretchy":1177},[588,1329,898],{},[598,1331,1183],{"stretchy":1177},[598,1333,1155],{},[588,1335,851],{},[598,1337,854],{},[588,1339,831],{"mathvariant":1162},[598,1341,854],{},[588,1343,898],{},[622,1345,1346],{"encoding":624},"\\operatorname{rg}(A) = \\dim \\operatorname{Bild} A",[569,1348,1350,1380],{"className":1349,"ariaHidden":630},[629],[569,1351,1353,1356,1362,1365,1368,1371,1374,1377],{"className":1352},[634],[569,1354],{"className":1355,"style":1252},[638],[569,1357,1359],{"className":1358},[873],[569,1360,1172],{"className":1361,"style":1259},[643,1230],[569,1363,1178],{"className":1364},[1263],[569,1366,898],{"className":1367},[643,644],[569,1369,1183],{"className":1370},[1270],[569,1372],{"className":1373,"style":684},[592],[569,1375,1155],{"className":1376},[672],[569,1378],{"className":1379,"style":684},[592],[569,1381,1383,1386,1389,1392,1398,1401],{"className":1382},[634],[569,1384],{"className":1385,"style":869},[638],[569,1387,851],{"className":1388},[873],[569,1390],{"className":1391,"style":665},[592],[569,1393,1395],{"className":1394},[873],[569,1396,831],{"className":1397},[643,1230],[569,1399],{"className":1400,"style":665},[592],[569,1402,898],{"className":1403},[643,644]," der Rang. Die Dimension des Kerns heißt auch ",[733,1406,1407],{},"Defekt",[565,1409,1410],{},"Folgerungen:",[1412,1413,1414,1644,1777],"ul",{},[1415,1416,1417,1445,1446,1559,1560,880],"li",{},[569,1418,1420,1433],{"className":1419},[572],[569,1421,1423],{"className":1422},[576],[578,1424,1425],{"xmlns":580},[582,1426,1427,1431],{},[585,1428,1429],{},[588,1430,590],{},[622,1432,590],{"encoding":624},[569,1434,1436],{"className":1435,"ariaHidden":630},[629],[569,1437,1439,1442],{"className":1438},[634],[569,1440],{"className":1441,"style":639},[638],[569,1443,590],{"className":1444,"style":645},[643,644]," ist genau dann injektiv, wenn ",[569,1447,1449,1481],{"className":1448},[572],[569,1450,1452],{"className":1451},[576],[578,1453,1454],{"xmlns":580},[582,1455,1456,1478],{},[585,1457,1458,1460,1462,1464,1466,1469,1475],{},[588,1459,735],{"mathvariant":1162},[598,1461,854],{},[588,1463,590],{},[598,1465,1155],{},[598,1467,1468],{"stretchy":1177},"{",[750,1470,1471,1473],{"accent":630},[753,1472,755],{},[598,1474,758],{},[598,1476,1477],{"stretchy":1177},"}",[622,1479,1480],{"encoding":624},"\\operatorname{Kern} f = \\{\\vec 0\\}",[569,1482,1484,1511],{"className":1483,"ariaHidden":630},[629],[569,1485,1487,1490,1496,1499,1502,1505,1508],{"className":1486},[634],[569,1488],{"className":1489,"style":639},[638],[569,1491,1493],{"className":1492},[873],[569,1494,735],{"className":1495},[643,1230],[569,1497],{"className":1498,"style":665},[592],[569,1500,590],{"className":1501,"style":645},[643,644],[569,1503],{"className":1504,"style":684},[592],[569,1506,1155],{"className":1507},[672],[569,1509],{"className":1510,"style":684},[592],[569,1512,1514,1518,1521,1556],{"className":1513},[634],[569,1515],{"className":1516,"style":1517},[638],"height:1.1774em;vertical-align:-0.25em;",[569,1519,1468],{"className":1520},[1263],[569,1522,1524],{"className":1523},[643,775],[569,1525,1527],{"className":1526},[779],[569,1528,1530],{"className":1529},[783],[569,1531,1533,1541],{"className":1532,"style":771},[787],[569,1534,1535,1538],{"style":790},[569,1536],{"className":1537,"style":795},[794],[569,1539,755],{"className":1540},[643],[569,1542,1543,1546],{"style":801},[569,1544],{"className":1545,"style":795},[794],[569,1547,1549],{"className":1548,"style":809},[808],[569,1550,1552],{"className":1551,"style":814},[813],[816,1553,1554],{"xmlns":818,"width":819,"height":820,"style":821,"viewBox":822,"preserveAspectRatio":823},[825,1555],{"d":827},[569,1557,1477],{"className":1558},[1270],", also wenn ",[569,1561,1563,1593],{"className":1562},[572],[569,1564,1566],{"className":1565},[576],[578,1567,1568],{"xmlns":580},[582,1569,1570,1590],{},[585,1571,1572,1574,1576,1578,1580,1582,1584,1586,1588],{},[588,1573,851],{},[598,1575,854],{},[588,1577,831],{"mathvariant":1162},[598,1579,854],{},[588,1581,590],{},[598,1583,1155],{},[588,1585,851],{},[598,1587,854],{},[588,1589,614],{},[622,1591,1592],{"encoding":624},"\\dim \\operatorname{Bild} f = \\dim V",[569,1594,1596,1629],{"className":1595,"ariaHidden":630},[629],[569,1597,1599,1602,1605,1608,1614,1617,1620,1623,1626],{"className":1598},[634],[569,1600],{"className":1601,"style":639},[638],[569,1603,851],{"className":1604},[873],[569,1606],{"className":1607,"style":665},[592],[569,1609,1611],{"className":1610},[873],[569,1612,831],{"className":1613},[643,1230],[569,1615],{"className":1616,"style":665},[592],[569,1618,590],{"className":1619,"style":645},[643,644],[569,1621],{"className":1622,"style":684},[592],[569,1624,1155],{"className":1625},[672],[569,1627],{"className":1628,"style":684},[592],[569,1630,1632,1635,1638,1641],{"className":1631},[634],[569,1633],{"className":1634,"style":869},[638],[569,1636,851],{"className":1637},[873],[569,1639],{"className":1640,"style":665},[592],[569,1642,614],{"className":1643,"style":680},[643,644],[1415,1645,1646,1647,1718,1719,1747,1748,1776],{},"Ist ",[569,1648,1650,1676],{"className":1649},[572],[569,1651,1653],{"className":1652},[576],[578,1654,1655],{"xmlns":580},[582,1656,1657,1673],{},[585,1658,1659,1661,1663,1665,1667,1669,1671],{},[588,1660,851],{},[598,1662,854],{},[588,1664,614],{},[598,1666,1155],{},[588,1668,851],{},[598,1670,854],{},[588,1672,620],{},[622,1674,1675],{"encoding":624},"\\dim V = \\dim W",[569,1677,1679,1703],{"className":1678,"ariaHidden":630},[629],[569,1680,1682,1685,1688,1691,1694,1697,1700],{"className":1681},[634],[569,1683],{"className":1684,"style":869},[638],[569,1686,851],{"className":1687},[873],[569,1689],{"className":1690,"style":665},[592],[569,1692,614],{"className":1693,"style":680},[643,644],[569,1695],{"className":1696,"style":684},[592],[569,1698,1155],{"className":1699},[672],[569,1701],{"className":1702,"style":684},[592],[569,1704,1706,1709,1712,1715],{"className":1705},[634],[569,1707],{"className":1708,"style":869},[638],[569,1710,851],{"className":1711},[873],[569,1713],{"className":1714,"style":665},[592],[569,1716,620],{"className":1717,"style":701},[643,644],", dann ist ",[569,1720,1722,1735],{"className":1721},[572],[569,1723,1725],{"className":1724},[576],[578,1726,1727],{"xmlns":580},[582,1728,1729,1733],{},[585,1730,1731],{},[588,1732,590],{},[622,1734,590],{"encoding":624},[569,1736,1738],{"className":1737,"ariaHidden":630},[629],[569,1739,1741,1744],{"className":1740},[634],[569,1742],{"className":1743,"style":639},[638],[569,1745,590],{"className":1746,"style":645},[643,644]," injektiv genau dann, wenn ",[569,1749,1751,1764],{"className":1750},[572],[569,1752,1754],{"className":1753},[576],[578,1755,1756],{"xmlns":580},[582,1757,1758,1762],{},[585,1759,1760],{},[588,1761,590],{},[622,1763,590],{"encoding":624},[569,1765,1767],{"className":1766,"ariaHidden":630},[629],[569,1768,1770,1773],{"className":1769},[634],[569,1771],{"className":1772,"style":639},[638],[569,1774,590],{"className":1775,"style":645},[643,644]," surjektiv ist.",[1415,1778,1646,1779,1852,1853,1881,1882,880],{},[569,1780,1782,1809],{"className":1781},[572],[569,1783,1785],{"className":1784},[576],[578,1786,1787],{"xmlns":580},[582,1788,1789,1806],{},[585,1790,1791,1793,1795,1797,1800,1802,1804],{},[588,1792,851],{},[598,1794,854],{},[588,1796,614],{},[598,1798,1799],{},">",[588,1801,851],{},[598,1803,854],{},[588,1805,620],{},[622,1807,1808],{"encoding":624},"\\dim V > \\dim W",[569,1810,1812,1837],{"className":1811,"ariaHidden":630},[629],[569,1813,1815,1819,1822,1825,1828,1831,1834],{"className":1814},[634],[569,1816],{"className":1817,"style":1818},[638],"height:0.7335em;vertical-align:-0.0391em;",[569,1820,851],{"className":1821},[873],[569,1823],{"className":1824,"style":665},[592],[569,1826,614],{"className":1827,"style":680},[643,644],[569,1829],{"className":1830,"style":684},[592],[569,1832,1799],{"className":1833},[672],[569,1835],{"className":1836,"style":684},[592],[569,1838,1840,1843,1846,1849],{"className":1839},[634],[569,1841],{"className":1842,"style":869},[638],[569,1844,851],{"className":1845},[873],[569,1847],{"className":1848,"style":665},[592],[569,1850,620],{"className":1851,"style":701},[643,644],", kann ",[569,1854,1856,1869],{"className":1855},[572],[569,1857,1859],{"className":1858},[576],[578,1860,1861],{"xmlns":580},[582,1862,1863,1867],{},[585,1864,1865],{},[588,1866,590],{},[622,1868,590],{"encoding":624},[569,1870,1872],{"className":1871,"ariaHidden":630},[629],[569,1873,1875,1878],{"className":1874},[634],[569,1876],{"className":1877,"style":639},[638],[569,1879,590],{"className":1880,"style":645},[643,644]," nicht injektiv sein, denn ",[569,1883,1885,1916],{"className":1884},[572],[569,1886,1888],{"className":1887},[576],[578,1889,1890],{"xmlns":580},[582,1891,1892,1913],{},[585,1893,1894,1896,1898,1900,1902,1904,1907,1909,1911],{},[588,1895,851],{},[598,1897,854],{},[588,1899,831],{"mathvariant":1162},[598,1901,854],{},[588,1903,590],{},[598,1905,1906],{},"≤",[588,1908,851],{},[598,1910,854],{},[588,1912,620],{},[622,1914,1915],{"encoding":624},"\\dim \\operatorname{Bild} f \\le \\dim W",[569,1917,1919,1952],{"className":1918,"ariaHidden":630},[629],[569,1920,1922,1925,1928,1931,1937,1940,1943,1946,1949],{"className":1921},[634],[569,1923],{"className":1924,"style":639},[638],[569,1926,851],{"className":1927},[873],[569,1929],{"className":1930,"style":665},[592],[569,1932,1934],{"className":1933},[873],[569,1935,831],{"className":1936},[643,1230],[569,1938],{"className":1939,"style":665},[592],[569,1941,590],{"className":1942,"style":645},[643,644],[569,1944],{"className":1945,"style":684},[592],[569,1947,1906],{"className":1948},[672],[569,1950],{"className":1951,"style":684},[592],[569,1953,1955,1958,1961,1964],{"className":1954},[634],[569,1956],{"className":1957,"style":869},[638],[569,1959,851],{"className":1960},[873],[569,1962],{"className":1963,"style":665},[592],[569,1965,620],{"className":1966,"style":701},[643,644],[565,1968,1969,1970,1998,1999,2027],{},"Die Formel setzt voraus, dass ",[569,1971,1973,1986],{"className":1972},[572],[569,1974,1976],{"className":1975},[576],[578,1977,1978],{"xmlns":580},[582,1979,1980,1984],{},[585,1981,1982],{},[588,1983,614],{},[622,1985,614],{"encoding":624},[569,1987,1989],{"className":1988,"ariaHidden":630},[629],[569,1990,1992,1995],{"className":1991},[634],[569,1993],{"className":1994,"style":697},[638],[569,1996,614],{"className":1997,"style":680},[643,644]," endlichdimensional ist. ",[569,2000,2002,2015],{"className":2001},[572],[569,2003,2005],{"className":2004},[576],[578,2006,2007],{"xmlns":580},[582,2008,2009,2013],{},[585,2010,2011],{},[588,2012,620],{},[622,2014,620],{"encoding":624},[569,2016,2018],{"className":2017,"ariaHidden":630},[629],[569,2019,2021,2024],{"className":2020},[634],[569,2022],{"className":2023,"style":697},[638],[569,2025,620],{"className":2026,"style":701},[643,644]," darf beliebig sein.",[560,2029,2031],{"id":2030},"beispiele","Beispiele",[565,2033,2034,2035,2324,2325,2397,2398,2518,2519,2601,2602,2682,2683,2917],{},"Für ",[569,2036,2038,2114],{"className":2037},[572],[569,2039,2041],{"className":2040},[576],[578,2042,2043],{"xmlns":580},[582,2044,2045,2111],{},[585,2046,2047,2049,2051],{},[588,2048,898],{},[598,2050,1155],{},[585,2052,2053,2055,2109],{},[598,2054,1178],{"fence":630},[2056,2057,2061,2087],"mtable",{"rowspacing":2058,"columnalign":2059,"columnspacing":2060},"0.16em","center center center","1em",[2062,2063,2064,2073,2080],"mtr",{},[2065,2066,2067],"mtd",{},[2068,2069,2070],"mstyle",{"scriptlevel":755,"displaystyle":1177},[753,2071,2072],{},"1",[2065,2074,2075],{},[2068,2076,2077],{"scriptlevel":755,"displaystyle":1177},[753,2078,2079],{},"2",[2065,2081,2082],{},[2068,2083,2084],{"scriptlevel":755,"displaystyle":1177},[753,2085,2086],{},"3",[2062,2088,2089,2095,2102],{},[2065,2090,2091],{},[2068,2092,2093],{"scriptlevel":755,"displaystyle":1177},[753,2094,2079],{},[2065,2096,2097],{},[2068,2098,2099],{"scriptlevel":755,"displaystyle":1177},[753,2100,2101],{},"4",[2065,2103,2104],{},[2068,2105,2106],{"scriptlevel":755,"displaystyle":1177},[753,2107,2108],{},"6",[598,2110,1183],{"fence":630},[622,2112,2113],{"encoding":624},"A = \\begin{pmatrix} 1 & 2 & 3 \\\\ 2 & 4 & 6 \\end{pmatrix}",[569,2115,2117,2135],{"className":2116,"ariaHidden":630},[629],[569,2118,2120,2123,2126,2129,2132],{"className":2119},[634],[569,2121],{"className":2122,"style":697},[638],[569,2124,898],{"className":2125},[643,644],[569,2127],{"className":2128,"style":684},[592],[569,2130,1155],{"className":2131},[672],[569,2133],{"className":2134,"style":684},[592],[569,2136,2138,2142],{"className":2137},[634],[569,2139],{"className":2140,"style":2141},[638],"height:2.4em;vertical-align:-0.95em;",[569,2143,2146,2155,2318],{"className":2144},[2145],"minner",[569,2147,2151],{"className":2148,"style":2150},[1263,2149],"delimcenter","top:0em;",[569,2152,1178],{"className":2153},[2154,984],"delimsizing",[569,2156,2158],{"className":2157},[643],[569,2159,2161,2214,2219,2222,2267,2270,2273],{"className":2160},[2056],[569,2162,2165],{"className":2163},[2164],"col-align-c",[569,2166,2169,2205],{"className":2167},[779,2168],"vlist-t2",[569,2170,2172,2200],{"className":2171},[783],[569,2173,2176,2188],{"className":2174,"style":2175},[787],"height:1.45em;",[569,2177,2179,2182],{"style":2178},"top:-3.61em;",[569,2180],{"className":2181,"style":795},[794],[569,2183,2185],{"className":2184},[643],[569,2186,2072],{"className":2187},[643],[569,2189,2191,2194],{"style":2190},"top:-2.41em;",[569,2192],{"className":2193,"style":795},[794],[569,2195,2197],{"className":2196},[643],[569,2198,2079],{"className":2199},[643],[569,2201,2204],{"className":2202},[2203],"vlist-s","​",[569,2206,2208],{"className":2207},[783],[569,2209,2212],{"className":2210,"style":2211},[787],"height:0.95em;",[569,2213],{},[569,2215],{"className":2216,"style":2218},[2217],"arraycolsep","width:0.5em;",[569,2220],{"className":2221,"style":2218},[2217],[569,2223,2225],{"className":2224},[2164],[569,2226,2228,2259],{"className":2227},[779,2168],[569,2229,2231,2256],{"className":2230},[783],[569,2232,2234,2245],{"className":2233,"style":2175},[787],[569,2235,2236,2239],{"style":2178},[569,2237],{"className":2238,"style":795},[794],[569,2240,2242],{"className":2241},[643],[569,2243,2079],{"className":2244},[643],[569,2246,2247,2250],{"style":2190},[569,2248],{"className":2249,"style":795},[794],[569,2251,2253],{"className":2252},[643],[569,2254,2101],{"className":2255},[643],[569,2257,2204],{"className":2258},[2203],[569,2260,2262],{"className":2261},[783],[569,2263,2265],{"className":2264,"style":2211},[787],[569,2266],{},[569,2268],{"className":2269,"style":2218},[2217],[569,2271],{"className":2272,"style":2218},[2217],[569,2274,2276],{"className":2275},[2164],[569,2277,2279,2310],{"className":2278},[779,2168],[569,2280,2282,2307],{"className":2281},[783],[569,2283,2285,2296],{"className":2284,"style":2175},[787],[569,2286,2287,2290],{"style":2178},[569,2288],{"className":2289,"style":795},[794],[569,2291,2293],{"className":2292},[643],[569,2294,2086],{"className":2295},[643],[569,2297,2298,2301],{"style":2190},[569,2299],{"className":2300,"style":795},[794],[569,2302,2304],{"className":2303},[643],[569,2305,2108],{"className":2306},[643],[569,2308,2204],{"className":2309},[2203],[569,2311,2313],{"className":2312},[783],[569,2314,2316],{"className":2315,"style":2211},[787],[569,2317],{},[569,2319,2321],{"className":2320,"style":2150},[1270,2149],[569,2322,1183],{"className":2323},[2154,984]," ist die zweite Zeile das Doppelte der ersten, also ",[569,2326,2328,2354],{"className":2327},[572],[569,2329,2331],{"className":2330},[576],[578,2332,2333],{"xmlns":580},[582,2334,2335,2351],{},[585,2336,2337,2339,2341,2343,2345,2347,2349],{},[588,2338,1172],{"mathvariant":1162},[598,2340,854],{},[598,2342,1178],{"stretchy":1177},[588,2344,898],{},[598,2346,1183],{"stretchy":1177},[598,2348,1155],{},[753,2350,2072],{},[622,2352,2353],{"encoding":624},"\\operatorname{rg}(A) = 1",[569,2355,2357,2387],{"className":2356,"ariaHidden":630},[629],[569,2358,2360,2363,2369,2372,2375,2378,2381,2384],{"className":2359},[634],[569,2361],{"className":2362,"style":1252},[638],[569,2364,2366],{"className":2365},[873],[569,2367,1172],{"className":2368,"style":1259},[643,1230],[569,2370,1178],{"className":2371},[1263],[569,2373,898],{"className":2374},[643,644],[569,2376,1183],{"className":2377},[1270],[569,2379],{"className":2380,"style":684},[592],[569,2382,1155],{"className":2383},[672],[569,2385],{"className":2386,"style":684},[592],[569,2388,2390,2394],{"className":2389},[634],[569,2391],{"className":2392,"style":2393},[638],"height:0.6444em;",[569,2395,2072],{"className":2396},[643],". Die Dimensionsformel liefert ",[569,2399,2401,2436],{"className":2400},[572],[569,2402,2404],{"className":2403},[576],[578,2405,2406],{"xmlns":580},[582,2407,2408,2433],{},[585,2409,2410,2412,2414,2416,2418,2420,2422,2424,2427,2429,2431],{},[588,2411,851],{},[598,2413,854],{},[588,2415,735],{"mathvariant":1162},[598,2417,854],{},[588,2419,898],{},[598,2421,1155],{},[753,2423,2086],{},[598,2425,2426],{},"−",[753,2428,2072],{},[598,2430,1155],{},[753,2432,2079],{},[622,2434,2435],{"encoding":624},"\\dim \\operatorname{Kern} A = 3 - 1 = 2",[569,2437,2439,2472,2491,2509],{"className":2438,"ariaHidden":630},[629],[569,2440,2442,2445,2448,2451,2457,2460,2463,2466,2469],{"className":2441},[634],[569,2443],{"className":2444,"style":869},[638],[569,2446,851],{"className":2447},[873],[569,2449],{"className":2450,"style":665},[592],[569,2452,2454],{"className":2453},[873],[569,2455,735],{"className":2456},[643,1230],[569,2458],{"className":2459,"style":665},[592],[569,2461,898],{"className":2462},[643,644],[569,2464],{"className":2465,"style":684},[592],[569,2467,1155],{"className":2468},[672],[569,2470],{"className":2471,"style":684},[592],[569,2473,2475,2479,2482,2485,2488],{"className":2474},[634],[569,2476],{"className":2477,"style":2478},[638],"height:0.7278em;vertical-align:-0.0833em;",[569,2480,2086],{"className":2481},[643],[569,2483],{"className":2484,"style":680},[592],[569,2486,2426],{"className":2487},[995],[569,2489],{"className":2490,"style":680},[592],[569,2492,2494,2497,2500,2503,2506],{"className":2493},[634],[569,2495],{"className":2496,"style":2393},[638],[569,2498,2072],{"className":2499},[643],[569,2501],{"className":2502,"style":684},[592],[569,2504,1155],{"className":2505},[672],[569,2507],{"className":2508,"style":684},[592],[569,2510,2512,2515],{"className":2511},[634],[569,2513],{"className":2514,"style":2393},[638],[569,2516,2079],{"className":2517},[643],". Tatsächlich bilden ",[569,2520,2522,2556],{"className":2521},[572],[569,2523,2525],{"className":2524},[576],[578,2526,2527],{"xmlns":580},[582,2528,2529,2553],{},[585,2530,2531,2533,2535,2537,2540,2543,2545,2547,2549,2551],{},[598,2532,1178],{"stretchy":1177},[598,2534,2426],{},[753,2536,2079],{},[598,2538,2539],{"separator":630},",",[603,2541,2542],{}," ",[753,2544,2072],{},[598,2546,2539],{"separator":630},[603,2548,2542],{},[753,2550,755],{},[598,2552,1183],{"stretchy":1177},[622,2554,2555],{"encoding":624},"(-2,\\ 1,\\ 0)",[569,2557,2559],{"className":2558,"ariaHidden":630},[629],[569,2560,2562,2565,2568,2571,2574,2577,2580,2583,2586,2589,2592,2595,2598],{"className":2561},[634],[569,2563],{"className":2564,"style":1252},[638],[569,2566,1178],{"className":2567},[1263],[569,2569,2426],{"className":2570},[643],[569,2572,2079],{"className":2573},[643],[569,2575,2539],{"className":2576},[657],[569,2578,2542],{"className":2579},[592],[569,2581],{"className":2582,"style":665},[592],[569,2584,2072],{"className":2585},[643],[569,2587,2539],{"className":2588},[657],[569,2590,2542],{"className":2591},[592],[569,2593],{"className":2594,"style":665},[592],[569,2596,755],{"className":2597},[643],[569,2599,1183],{"className":2600},[1270]," und ",[569,2603,2605,2637],{"className":2604},[572],[569,2606,2608],{"className":2607},[576],[578,2609,2610],{"xmlns":580},[582,2611,2612,2634],{},[585,2613,2614,2616,2618,2620,2622,2624,2626,2628,2630,2632],{},[598,2615,1178],{"stretchy":1177},[598,2617,2426],{},[753,2619,2086],{},[598,2621,2539],{"separator":630},[603,2623,2542],{},[753,2625,755],{},[598,2627,2539],{"separator":630},[603,2629,2542],{},[753,2631,2072],{},[598,2633,1183],{"stretchy":1177},[622,2635,2636],{"encoding":624},"(-3,\\ 0,\\ 1)",[569,2638,2640],{"className":2639,"ariaHidden":630},[629],[569,2641,2643,2646,2649,2652,2655,2658,2661,2664,2667,2670,2673,2676,2679],{"className":2642},[634],[569,2644],{"className":2645,"style":1252},[638],[569,2647,1178],{"className":2648},[1263],[569,2650,2426],{"className":2651},[643],[569,2653,2086],{"className":2654},[643],[569,2656,2539],{"className":2657},[657],[569,2659,2542],{"className":2660},[592],[569,2662],{"className":2663,"style":665},[592],[569,2665,755],{"className":2666},[643],[569,2668,2539],{"className":2669},[657],[569,2671,2542],{"className":2672},[592],[569,2674],{"className":2675,"style":665},[592],[569,2677,2072],{"className":2678},[643],[569,2680,1183],{"className":2681},[1270]," eine Basis des Kerns: Beide lösen ",[569,2684,2686,2729],{"className":2685},[572],[569,2687,2689],{"className":2688},[576],[578,2690,2691],{"xmlns":580},[582,2692,2693,2726],{},[585,2694,2695,2702,2704,2706,2712,2714,2716,2722,2724],{},[2696,2697,2698,2700],"msub",{},[588,2699,1016],{},[753,2701,2072],{},[598,2703,1169],{},[753,2705,2079],{},[2696,2707,2708,2710],{},[588,2709,1016],{},[753,2711,2079],{},[598,2713,1169],{},[753,2715,2086],{},[2696,2717,2718,2720],{},[588,2719,1016],{},[753,2721,2086],{},[598,2723,1155],{},[753,2725,755],{},[622,2727,2728],{"encoding":624},"x_1 + 2x_2 + 3x_3 = 0",[569,2730,2732,2791,2850,2908],{"className":2731,"ariaHidden":630},[629],[569,2733,2735,2739,2782,2785,2788],{"className":2734},[634],[569,2736],{"className":2737,"style":2738},[638],"height:0.7333em;vertical-align:-0.15em;",[569,2740,2742,2745],{"className":2741},[643],[569,2743,1016],{"className":2744},[643,644],[569,2746,2748],{"className":2747},[962],[569,2749,2751,2773],{"className":2750},[779,2168],[569,2752,2754,2770],{"className":2753},[783],[569,2755,2758],{"className":2756,"style":2757},[787],"height:0.3011em;",[569,2759,2761,2764],{"style":2760},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[569,2762],{"className":2763,"style":978},[794],[569,2765,2767],{"className":2766},[982,983,984,985],[569,2768,2072],{"className":2769},[643,985],[569,2771,2204],{"className":2772},[2203],[569,2774,2776],{"className":2775},[783],[569,2777,2780],{"className":2778,"style":2779},[787],"height:0.15em;",[569,2781],{},[569,2783],{"className":2784,"style":680},[592],[569,2786,1169],{"className":2787},[995],[569,2789],{"className":2790,"style":680},[592],[569,2792,2794,2798,2801,2841,2844,2847],{"className":2793},[634],[569,2795],{"className":2796,"style":2797},[638],"height:0.7944em;vertical-align:-0.15em;",[569,2799,2079],{"className":2800},[643],[569,2802,2804,2807],{"className":2803},[643],[569,2805,1016],{"className":2806},[643,644],[569,2808,2810],{"className":2809},[962],[569,2811,2813,2833],{"className":2812},[779,2168],[569,2814,2816,2830],{"className":2815},[783],[569,2817,2819],{"className":2818,"style":2757},[787],[569,2820,2821,2824],{"style":2760},[569,2822],{"className":2823,"style":978},[794],[569,2825,2827],{"className":2826},[982,983,984,985],[569,2828,2079],{"className":2829},[643,985],[569,2831,2204],{"className":2832},[2203],[569,2834,2836],{"className":2835},[783],[569,2837,2839],{"className":2838,"style":2779},[787],[569,2840],{},[569,2842],{"className":2843,"style":680},[592],[569,2845,1169],{"className":2846},[995],[569,2848],{"className":2849,"style":680},[592],[569,2851,2853,2856,2859,2899,2902,2905],{"className":2852},[634],[569,2854],{"className":2855,"style":2797},[638],[569,2857,2086],{"className":2858},[643],[569,2860,2862,2865],{"className":2861},[643],[569,2863,1016],{"className":2864},[643,644],[569,2866,2868],{"className":2867},[962],[569,2869,2871,2891],{"className":2870},[779,2168],[569,2872,2874,2888],{"className":2873},[783],[569,2875,2877],{"className":2876,"style":2757},[787],[569,2878,2879,2882],{"style":2760},[569,2880],{"className":2881,"style":978},[794],[569,2883,2885],{"className":2884},[982,983,984,985],[569,2886,2086],{"className":2887},[643,985],[569,2889,2204],{"className":2890},[2203],[569,2892,2894],{"className":2893},[783],[569,2895,2897],{"className":2896,"style":2779},[787],[569,2898],{},[569,2900],{"className":2901,"style":684},[592],[569,2903,1155],{"className":2904},[672],[569,2906],{"className":2907,"style":684},[592],[569,2909,2911,2914],{"className":2910},[634],[569,2912],{"className":2913,"style":2393},[638],[569,2915,755],{"className":2916},[643]," und sind linear unabhängig.",[565,2919,2920,2921,3025,3026,3054,3055,3116,3117,3156,3157,3054,3185,3224,3225,880],{},"Die Ableitung ",[569,2922,2924,2954],{"className":2923},[572],[569,2925,2927],{"className":2926},[576],[578,2928,2929],{"xmlns":580},[582,2930,2931,2951],{},[585,2932,2933,2936,2938,2940,2942,2944],{},[588,2934,2935],{},"D",[598,2937,1178],{"stretchy":1177},[588,2939,565],{},[598,2941,1183],{"stretchy":1177},[598,2943,1155],{},[903,2945,2946,2948],{},[588,2947,565],{},[598,2949,2950],{"mathvariant":1162,"lspace":600,"rspace":600},"′",[622,2952,2953],{"encoding":624},"D(p) = p'",[569,2955,2957,2985],{"className":2956,"ariaHidden":630},[629],[569,2958,2960,2963,2967,2970,2973,2976,2979,2982],{"className":2959},[634],[569,2961],{"className":2962,"style":1252},[638],[569,2964,2935],{"className":2965,"style":2966},[643,644],"margin-right:0.0278em;",[569,2968,1178],{"className":2969},[1263],[569,2971,565],{"className":2972},[643,644],[569,2974,1183],{"className":2975},[1270],[569,2977],{"className":2978,"style":684},[592],[569,2980,1155],{"className":2981},[672],[569,2983],{"className":2984,"style":684},[592],[569,2986,2988,2992],{"className":2987},[634],[569,2989],{"className":2990,"style":2991},[638],"height:0.9463em;vertical-align:-0.1944em;",[569,2993,2995,2998],{"className":2994},[643],[569,2996,565],{"className":2997},[643,644],[569,2999,3001],{"className":3000},[962],[569,3002,3004],{"className":3003},[779],[569,3005,3007],{"className":3006},[783],[569,3008,3011],{"className":3009,"style":3010},[787],"height:0.7519em;",[569,3012,3013,3016],{"style":974},[569,3014],{"className":3015,"style":978},[794],[569,3017,3019],{"className":3018},[982,983,984,985],[569,3020,3022],{"className":3021},[643,985],[569,3023,2950],{"className":3024},[643,985]," auf den Polynomen vom Grad höchstens ",[569,3027,3029,3042],{"className":3028},[572],[569,3030,3032],{"className":3031},[576],[578,3033,3034],{"xmlns":580},[582,3035,3036,3040],{},[585,3037,3038],{},[753,3039,2086],{},[622,3041,2086],{"encoding":624},[569,3043,3045],{"className":3044,"ariaHidden":630},[629],[569,3046,3048,3051],{"className":3047},[634],[569,3049],{"className":3050,"style":2393},[638],[569,3052,2086],{"className":3053},[643]," (",[569,3056,3058,3080],{"className":3057},[572],[569,3059,3061],{"className":3060},[576],[578,3062,3063],{"xmlns":580},[582,3064,3065,3077],{},[585,3066,3067,3069,3071,3073,3075],{},[588,3068,851],{},[598,3070,854],{},[588,3072,614],{},[598,3074,1155],{},[753,3076,2101],{},[622,3078,3079],{"encoding":624},"\\dim V = 4",[569,3081,3083,3107],{"className":3082,"ariaHidden":630},[629],[569,3084,3086,3089,3092,3095,3098,3101,3104],{"className":3085},[634],[569,3087],{"className":3088,"style":869},[638],[569,3090,851],{"className":3091},[873],[569,3093],{"className":3094,"style":665},[592],[569,3096,614],{"className":3097,"style":680},[643,644],[569,3099],{"className":3100,"style":684},[592],[569,3102,1155],{"className":3103},[672],[569,3105],{"className":3106,"style":684},[592],[569,3108,3110,3113],{"className":3109},[634],[569,3111],{"className":3112,"style":2393},[638],[569,3114,2101],{"className":3115},[643],"): Der Kern sind die Konstanten (",[569,3118,3120,3138],{"className":3119},[572],[569,3121,3123],{"className":3122},[576],[578,3124,3125],{"xmlns":580},[582,3126,3127,3135],{},[585,3128,3129,3131,3133],{},[588,3130,851],{},[598,3132,854],{},[753,3134,2072],{},[622,3136,3137],{"encoding":624},"\\dim 1",[569,3139,3141],{"className":3140,"ariaHidden":630},[629],[569,3142,3144,3147,3150,3153],{"className":3143},[634],[569,3145],{"className":3146,"style":869},[638],[569,3148,851],{"className":3149},[873],[569,3151],{"className":3152,"style":665},[592],[569,3154,2072],{"className":3155},[643],"), das Bild sind die Polynome vom Grad höchstens ",[569,3158,3160,3173],{"className":3159},[572],[569,3161,3163],{"className":3162},[576],[578,3164,3165],{"xmlns":580},[582,3166,3167,3171],{},[585,3168,3169],{},[753,3170,2079],{},[622,3172,2079],{"encoding":624},[569,3174,3176],{"className":3175,"ariaHidden":630},[629],[569,3177,3179,3182],{"className":3178},[634],[569,3180],{"className":3181,"style":2393},[638],[569,3183,2079],{"className":3184},[643],[569,3186,3188,3206],{"className":3187},[572],[569,3189,3191],{"className":3190},[576],[578,3192,3193],{"xmlns":580},[582,3194,3195,3203],{},[585,3196,3197,3199,3201],{},[588,3198,851],{},[598,3200,854],{},[753,3202,2086],{},[622,3204,3205],{"encoding":624},"\\dim 3",[569,3207,3209],{"className":3208,"ariaHidden":630},[629],[569,3210,3212,3215,3218,3221],{"className":3211},[634],[569,3213],{"className":3214,"style":869},[638],[569,3216,851],{"className":3217},[873],[569,3219],{"className":3220,"style":665},[592],[569,3222,2086],{"className":3223},[643],"). Es gilt ",[569,3226,3228,3250],{"className":3227},[572],[569,3229,3231],{"className":3230},[576],[578,3232,3233],{"xmlns":580},[582,3234,3235,3247],{},[585,3236,3237,3239,3241,3243,3245],{},[753,3238,2101],{},[598,3240,1155],{},[753,3242,2072],{},[598,3244,1169],{},[753,3246,2086],{},[622,3248,3249],{"encoding":624},"4 = 1 + 3",[569,3251,3253,3271,3289],{"className":3252,"ariaHidden":630},[629],[569,3254,3256,3259,3262,3265,3268],{"className":3255},[634],[569,3257],{"className":3258,"style":2393},[638],[569,3260,2101],{"className":3261},[643],[569,3263],{"className":3264,"style":684},[592],[569,3266,1155],{"className":3267},[672],[569,3269],{"className":3270,"style":684},[592],[569,3272,3274,3277,3280,3283,3286],{"className":3273},[634],[569,3275],{"className":3276,"style":2478},[638],[569,3278,2072],{"className":3279},[643],[569,3281],{"className":3282,"style":680},[592],[569,3284,1169],{"className":3285},[995],[569,3287],{"className":3288,"style":680},[592],[569,3290,3292,3295],{"className":3291},[634],[569,3293],{"className":3294,"style":2393},[638],[569,3296,2086],{"className":3297},[643],[565,3299,3300,3301,3414,3415,3489,3490,3609],{},"Jede lineare Abbildung ",[569,3302,3304,3331],{"className":3303},[572],[569,3305,3307],{"className":3306},[576],[578,3308,3309],{"xmlns":580},[582,3310,3311,3328],{},[585,3312,3313,3320,3322],{},[903,3314,3315,3317],{},[588,3316,908],{"mathvariant":907},[753,3318,3319],{},"5",[598,3321,617],{},[903,3323,3324,3326],{},[588,3325,908],{"mathvariant":907},[753,3327,2086],{},[622,3329,3330],{"encoding":624},"\\mathbb{R}^5 \\to \\mathbb{R}^3",[569,3332,3334,3379],{"className":3333,"ariaHidden":630},[629],[569,3335,3337,3341,3370,3373,3376],{"className":3336},[634],[569,3338],{"className":3339,"style":3340},[638],"height:0.8141em;",[569,3342,3344,3347],{"className":3343},[643],[569,3345,908],{"className":3346},[643,958],[569,3348,3350],{"className":3349},[962],[569,3351,3353],{"className":3352},[779],[569,3354,3356],{"className":3355},[783],[569,3357,3359],{"className":3358,"style":3340},[787],[569,3360,3361,3364],{"style":974},[569,3362],{"className":3363,"style":978},[794],[569,3365,3367],{"className":3366},[982,983,984,985],[569,3368,3319],{"className":3369},[643,985],[569,3371],{"className":3372,"style":684},[592],[569,3374,617],{"className":3375},[672],[569,3377],{"className":3378,"style":684},[592],[569,3380,3382,3385],{"className":3381},[634],[569,3383],{"className":3384,"style":3340},[638],[569,3386,3388,3391],{"className":3387},[643],[569,3389,908],{"className":3390},[643,958],[569,3392,3394],{"className":3393},[962],[569,3395,3397],{"className":3396},[779],[569,3398,3400],{"className":3399},[783],[569,3401,3403],{"className":3402,"style":3340},[787],[569,3404,3405,3408],{"style":974},[569,3406],{"className":3407,"style":978},[794],[569,3409,3411],{"className":3410},[982,983,984,985],[569,3412,2086],{"className":3413},[643,985]," hat ",[569,3416,3418,3444],{"className":3417},[572],[569,3419,3421],{"className":3420},[576],[578,3422,3423],{"xmlns":580},[582,3424,3425,3441],{},[585,3426,3427,3429,3431,3433,3435,3437,3439],{},[588,3428,851],{},[598,3430,854],{},[588,3432,831],{"mathvariant":1162},[598,3434,854],{},[588,3436,590],{},[598,3438,1906],{},[753,3440,2086],{},[622,3442,3443],{"encoding":624},"\\dim \\operatorname{Bild} f \\le 3",[569,3445,3447,3480],{"className":3446,"ariaHidden":630},[629],[569,3448,3450,3453,3456,3459,3465,3468,3471,3474,3477],{"className":3449},[634],[569,3451],{"className":3452,"style":639},[638],[569,3454,851],{"className":3455},[873],[569,3457],{"className":3458,"style":665},[592],[569,3460,3462],{"className":3461},[873],[569,3463,831],{"className":3464},[643,1230],[569,3466],{"className":3467,"style":665},[592],[569,3469,590],{"className":3470,"style":645},[643,644],[569,3472],{"className":3473,"style":684},[592],[569,3475,1906],{"className":3476},[672],[569,3478],{"className":3479,"style":684},[592],[569,3481,3483,3486],{"className":3482},[634],[569,3484],{"className":3485,"style":2393},[638],[569,3487,2086],{"className":3488},[643],", also ",[569,3491,3493,3528],{"className":3492},[572],[569,3494,3496],{"className":3495},[576],[578,3497,3498],{"xmlns":580},[582,3499,3500,3525],{},[585,3501,3502,3504,3506,3508,3510,3512,3515,3517,3519,3521,3523],{},[588,3503,851],{},[598,3505,854],{},[588,3507,735],{"mathvariant":1162},[598,3509,854],{},[588,3511,590],{},[598,3513,3514],{},"≥",[753,3516,3319],{},[598,3518,2426],{},[753,3520,2086],{},[598,3522,1155],{},[753,3524,2079],{},[622,3526,3527],{"encoding":624},"\\dim \\operatorname{Kern} f \\ge 5 - 3 = 2",[569,3529,3531,3564,3582,3600],{"className":3530,"ariaHidden":630},[629],[569,3532,3534,3537,3540,3543,3549,3552,3555,3558,3561],{"className":3533},[634],[569,3535],{"className":3536,"style":639},[638],[569,3538,851],{"className":3539},[873],[569,3541],{"className":3542,"style":665},[592],[569,3544,3546],{"className":3545},[873],[569,3547,735],{"className":3548},[643,1230],[569,3550],{"className":3551,"style":665},[592],[569,3553,590],{"className":3554,"style":645},[643,644],[569,3556],{"className":3557,"style":684},[592],[569,3559,3514],{"className":3560},[672],[569,3562],{"className":3563,"style":684},[592],[569,3565,3567,3570,3573,3576,3579],{"className":3566},[634],[569,3568],{"className":3569,"style":2478},[638],[569,3571,3319],{"className":3572},[643],[569,3574],{"className":3575,"style":680},[592],[569,3577,2426],{"className":3578},[995],[569,3580],{"className":3581,"style":680},[592],[569,3583,3585,3588,3591,3594,3597],{"className":3584},[634],[569,3586],{"className":3587,"style":2393},[638],[569,3589,2086],{"className":3590},[643],[569,3592],{"className":3593,"style":684},[592],[569,3595,1155],{"className":3596},[672],[569,3598],{"className":3599,"style":684},[592],[569,3601,3603,3606],{"className":3602},[634],[569,3604],{"className":3605,"style":2393},[638],[569,3607,2079],{"className":3608},[643],". Ein homogenes System mit 3 Gleichungen und 5 Unbekannten hat deshalb immer mindestens 2 freie Parameter.",[560,3611,3613],{"id":3612},"typische-fehler","Typische Fehler",[1412,3615,3616,3889,3970],{},[1415,3617,3618,3619,3714,3715,3743,3744,3772,3773,880],{},"Bei ",[569,3620,3622,3649],{"className":3621},[572],[569,3623,3625],{"className":3624},[576],[578,3626,3627],{"xmlns":580},[582,3628,3629,3647],{},[585,3630,3631,3633,3635],{},[588,3632,898],{},[598,3634,901],{},[903,3636,3637,3639],{},[588,3638,908],{"mathvariant":907},[585,3640,3641,3643,3645],{},[588,3642,913],{},[598,3644,916],{},[588,3646,919],{},[622,3648,922],{"encoding":624},[569,3650,3652,3670],{"className":3651,"ariaHidden":630},[629],[569,3653,3655,3658,3661,3664,3667],{"className":3654},[634],[569,3656],{"className":3657,"style":932},[638],[569,3659,898],{"className":3660},[643,644],[569,3662],{"className":3663,"style":684},[592],[569,3665,901],{"className":3666},[672],[569,3668],{"className":3669,"style":684},[592],[569,3671,3673,3676],{"className":3672},[634],[569,3674],{"className":3675,"style":951},[638],[569,3677,3679,3682],{"className":3678},[643],[569,3680,908],{"className":3681},[643,958],[569,3683,3685],{"className":3684},[962],[569,3686,3688],{"className":3687},[779],[569,3689,3691],{"className":3690},[783],[569,3692,3694],{"className":3693,"style":951},[787],[569,3695,3696,3699],{"style":974},[569,3697],{"className":3698,"style":978},[794],[569,3700,3702],{"className":3701},[982,983,984,985],[569,3703,3705,3708,3711],{"className":3704},[643,985],[569,3706,913],{"className":3707},[643,644,985],[569,3709,916],{"className":3710},[995,985],[569,3712,919],{"className":3713},[643,644,985]," die Zeilenzahl ",[569,3716,3718,3731],{"className":3717},[572],[569,3719,3721],{"className":3720},[576],[578,3722,3723],{"xmlns":580},[582,3724,3725,3729],{},[585,3726,3727],{},[588,3728,913],{},[622,3730,913],{"encoding":624},[569,3732,3734],{"className":3733,"ariaHidden":630},[629],[569,3735,3737,3740],{"className":3736},[634],[569,3738],{"className":3739,"style":1198},[638],[569,3741,913],{"className":3742},[643,644]," statt der Spaltenzahl ",[569,3745,3747,3760],{"className":3746},[572],[569,3748,3750],{"className":3749},[576],[578,3751,3752],{"xmlns":580},[582,3753,3754,3758],{},[585,3755,3756],{},[588,3757,919],{},[622,3759,919],{"encoding":624},[569,3761,3763],{"className":3762,"ariaHidden":630},[629],[569,3764,3766,3769],{"className":3765},[634],[569,3767],{"className":3768,"style":1198},[638],[569,3770,919],{"className":3771},[643,644]," einsetzen. Richtig: ",[569,3774,3776,3814],{"className":3775},[572],[569,3777,3779],{"className":3778},[576],[578,3780,3781],{"xmlns":580},[582,3782,3783,3811],{},[585,3784,3785,3787,3789,3791,3793,3795,3797,3799,3801,3803,3805,3807,3809],{},[588,3786,919],{},[598,3788,1155],{},[588,3790,851],{},[598,3792,854],{},[588,3794,735],{"mathvariant":1162},[598,3796,854],{},[588,3798,898],{},[598,3800,1169],{},[588,3802,1172],{"mathvariant":1162},[598,3804,854],{},[598,3806,1178],{"stretchy":1177},[588,3808,898],{},[598,3810,1183],{"stretchy":1177},[622,3812,3813],{"encoding":624},"n = \\dim \\operatorname{Kern} A + \\operatorname{rg}(A)",[569,3815,3817,3835,3868],{"className":3816,"ariaHidden":630},[629],[569,3818,3820,3823,3826,3829,3832],{"className":3819},[634],[569,3821],{"className":3822,"style":1198},[638],[569,3824,919],{"className":3825},[643,644],[569,3827],{"className":3828,"style":684},[592],[569,3830,1155],{"className":3831},[672],[569,3833],{"className":3834,"style":684},[592],[569,3836,3838,3841,3844,3847,3853,3856,3859,3862,3865],{"className":3837},[634],[569,3839],{"className":3840,"style":1217},[638],[569,3842,851],{"className":3843},[873],[569,3845],{"className":3846,"style":665},[592],[569,3848,3850],{"className":3849},[873],[569,3851,735],{"className":3852},[643,1230],[569,3854],{"className":3855,"style":665},[592],[569,3857,898],{"className":3858},[643,644],[569,3860],{"className":3861,"style":680},[592],[569,3863,1169],{"className":3864},[995],[569,3866],{"className":3867,"style":680},[592],[569,3869,3871,3874,3880,3883,3886],{"className":3870},[634],[569,3872],{"className":3873,"style":1252},[638],[569,3875,3877],{"className":3876},[873],[569,3878,1172],{"className":3879,"style":1259},[643,1230],[569,3881,1178],{"className":3882},[1263],[569,3884,898],{"className":3885},[643,644],[569,3887,1183],{"className":3888},[1270],[1415,3890,3891,3930,3931,3969],{},[569,3892,3894,3912],{"className":3893},[572],[569,3895,3897],{"className":3896},[576],[578,3898,3899],{"xmlns":580},[582,3900,3901,3909],{},[585,3902,3903,3905,3907],{},[588,3904,851],{},[598,3906,854],{},[588,3908,620],{},[622,3910,3911],{"encoding":624},"\\dim W",[569,3913,3915],{"className":3914,"ariaHidden":630},[629],[569,3916,3918,3921,3924,3927],{"className":3917},[634],[569,3919],{"className":3920,"style":869},[638],[569,3922,851],{"className":3923},[873],[569,3925],{"className":3926,"style":665},[592],[569,3928,620],{"className":3929,"style":701},[643,644]," statt ",[569,3932,3934,3951],{"className":3933},[572],[569,3935,3937],{"className":3936},[576],[578,3938,3939],{"xmlns":580},[582,3940,3941,3949],{},[585,3942,3943,3945,3947],{},[588,3944,851],{},[598,3946,854],{},[588,3948,614],{},[622,3950,859],{"encoding":624},[569,3952,3954],{"className":3953,"ariaHidden":630},[629],[569,3955,3957,3960,3963,3966],{"className":3956},[634],[569,3958],{"className":3959,"style":869},[638],[569,3961,851],{"className":3962},[873],[569,3964],{"className":3965,"style":665},[592],[569,3967,614],{"className":3968,"style":680},[643,644]," auf die linke Seite schreiben. Die Formel bezieht sich auf den Definitionsraum.",[1415,3971,3972,3973,4025,4026,3489,4029,4057],{},"Die Dimension des Kerns mit der Anzahl der Nullzeilen in der Stufenform verwechseln. Bei nicht quadratischen Matrizen gilt: ",[569,3974,3976,3998],{"className":3975},[572],[569,3977,3979],{"className":3978},[576],[578,3980,3981],{"xmlns":580},[582,3982,3983,3995],{},[585,3984,3985,3987,3989,3991,3993],{},[588,3986,851],{},[598,3988,854],{},[588,3990,735],{"mathvariant":1162},[598,3992,854],{},[588,3994,898],{},[622,3996,3997],{"encoding":624},"\\dim \\operatorname{Kern} A",[569,3999,4001],{"className":4000,"ariaHidden":630},[629],[569,4002,4004,4007,4010,4013,4019,4022],{"className":4003},[634],[569,4005],{"className":4006,"style":869},[638],[569,4008,851],{"className":4009},[873],[569,4011],{"className":4012,"style":665},[592],[569,4014,4016],{"className":4015},[873],[569,4017,735],{"className":4018},[643,1230],[569,4020],{"className":4021,"style":665},[592],[569,4023,898],{"className":4024},[643,644]," ist die Zahl der ",[733,4027,4028],{},"freien Variablen",[569,4030,4032,4045],{"className":4031},[572],[569,4033,4035],{"className":4034},[576],[578,4036,4037],{"xmlns":580},[582,4038,4039,4043],{},[585,4040,4041],{},[588,4042,919],{},[622,4044,919],{"encoding":624},[569,4046,4048],{"className":4047,"ariaHidden":630},[629],[569,4049,4051,4054],{"className":4050},[634],[569,4052],{"className":4053,"style":1198},[638],[569,4055,919],{"className":4056},[643,644]," minus Zahl der Stufen.",{"title":4059,"searchDepth":4060,"depth":4060,"links":4061},"",2,[4062,4063,4064],{"id":562,"depth":4060,"text":563},{"id":2030,"depth":4060,"text":2031},{"id":3612,"depth":4060,"text":3613},[4066,4068,4070,4072,4074,4076,4078,4080],{"lhs":4067,"rhs":2086},"1 + 2",{"lhs":4069,"rhs":755},"1*(-2) + 2*1 + 3*0",{"lhs":4071,"rhs":755},"2*(-2) + 4*1 + 6*0",{"lhs":4073,"rhs":755},"1*(-3) + 2*0 + 3*1",{"lhs":4075,"rhs":755},"2*(-3) + 4*0 + 6*1",{"lhs":4077,"rhs":755},"multiply([[1, 2, 3], [2, 4, 6]], [-2, 1, 0])[1]",{"lhs":2101,"rhs":4079},"1 + 3",{"lhs":4081,"rhs":2079},"5 - 3","f\\colon V \\to W \\text{ linear},\\ \\dim V \u003C \\infty","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmspace>\u003C\u002Fmspace>\u003Cmspace width=\"0.1111em\"\u002F>\u003Cmo lspace=\"0em\" rspace=\"0.17em\">\u003C\u002Fmo>\u003Cmtext> ⁣\u003C\u002Fmtext>\u003Cmo lspace=\"0em\" rspace=\"0em\">:\u003C\u002Fmo>\u003Cmspace width=\"0.3333em\"\u002F>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi>W\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\\colon V \\to W\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\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1111em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:-0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.3333em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">W\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">linear\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>dim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>V\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\dim V < \\infty\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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">dim\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","rank-nullity","\\dim V = \\dim \\operatorname{Kern} f + \\dim \\operatorname{Bild} f","\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>dim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>V\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>dim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Kern\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>dim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">Bild\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\dim V = \\dim \\operatorname{Kern} f + \\dim \\operatorname{Bild} f\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">dim\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">V\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=\"mop\">dim\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">Kern\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\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=\"mop\">dim\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mord mathrm\">Bild\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdimensionsformel",[],[4095,4096,4097,4098],"matrix-rank","linear-system-solvability","linear-map-matrix","gaussian-elimination",{"title":548,"description":4059},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdimensionsformel","Die Dimension des Definitionsraums einer linearen Abbildung ist die Summe der Dimensionen von Kern und Bild.",[4103,4104,4105,4106,4107],"dimension","kern","bild","rang","lineare abbildung",[4109,4112,4115,4118,4122,4126],{"symbol":590,"meaning":4110,"symbolHtml":4111},"lineare Abbildung von V nach W","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\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\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":614,"meaning":4113,"symbolHtml":4114},"endlichdimensionaler Vektorraum, der Definitionsbereich von f","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>V\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">V\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\" style=\"margin-right:0.2222em;\">V\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":620,"meaning":4116,"symbolHtml":4117},"Vektorraum, in dem die Bilder von f liegen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>W\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">W\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\" style=\"margin-right:0.1389em;\">W\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4119,"meaning":4120,"symbolHtml":4121},"\\operatorname{Kern} f","Kern von f, alle Vektoren v mit f(v) = 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Kern\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{Kern} f\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=\"mop\">\u003Cspan class=\"mord mathrm\">Kern\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4123,"meaning":4124,"symbolHtml":4125},"\\operatorname{Bild} f","Bild von f, alle Vektoren f(v) mit v aus V","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Bild\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\operatorname{Bild} f\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=\"mop\">\u003Cspan class=\"mord mathrm\">Bild\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4127,"meaning":4128,"symbolHtml":4129},"\\dim","Dimension, die Anzahl der Vektoren einer Basis","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>dim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\dim\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">dim\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","35v6zPyTWXdGn1SKdUJYuTLZd3kQdHv_BcDsEMddOFU",[4132,4135,4138,4141],{"stem":4133,"title":4134,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdarstellungsmatrix","Darstellungsmatrix einer linearen Abbildung",{"stem":4136,"title":4137,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgauss-algorithmus","Gauß-Algorithmus",{"stem":4139,"title":4140,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Floesbarkeit-linearer-gleichungssysteme","Lösbarkeit linearer Gleichungssysteme",{"stem":4142,"title":4143,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Frang-einer-matrix","Rang einer Matrix",1793824277754]