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Die Zahl ",[574,988,990,1004],{"className":989},[577],[574,991,993],{"className":992},[581],[583,994,995],{"xmlns":585},[587,996,997,1001],{},[590,998,999],{},[593,1000,876],{},[597,1002,1003],{"encoding":599},"\\lambda",[574,1005,1007],{"className":1006,"ariaHidden":604},[603],[574,1008,1010,1014],{"className":1009},[608],[574,1011],{"className":1012,"style":1013},[612],"height:0.6944em;",[574,1015,876],{"className":1016},[617,618]," heißt ",[569,1019,1020],{},"Eigenwert",".",[565,1023,1024,1025,1201,1202,1357,1358,1415,1416,1515,1516,1546,1547,1575,1576,1579,1580,1021],{},"Umgeformt lautet die Bedingung ",[574,1026,1028,1071],{"className":1027},[577],[574,1029,1031],{"className":1030},[581],[583,1032,1033],{"xmlns":585},[587,1034,1035,1068],{},[590,1036,1037,1041,1043,1046,1048,1051,1054,1060,1062],{},[639,1038,1040],{"stretchy":1039},"false","(",[593,1042,595],{},[639,1044,1045],{},"−",[593,1047,876],{},[593,1049,1050],{},"E",[639,1052,1053],{"stretchy":1039},")",[633,1055,1056,1058],{"accent":604},[593,1057,637],{},[639,1059,641],{},[639,1061,774],{},[633,1063,1064,1066],{"accent":604},[649,1065,651],{},[639,1067,641],{},[597,1069,1070],{"encoding":599},"(A - \\lambda E)\\vec{v} = \\vec{0}",[574,1072,1074,1099,1160],{"className":1073,"ariaHidden":604},[603],[574,1075,1077,1081,1085,1088,1092,1096],{"className":1076},[608],[574,1078],{"className":1079,"style":1080},[612],"height:1em;vertical-align:-0.25em;",[574,1082,1040],{"className":1083},[1084],"mopen",[574,1086,595],{"className":1087},[617,618],[574,1089],{"className":1090,"style":1091},[727],"margin-right:0.2222em;",[574,1093,1045],{"className":1094},[1095],"mbin",[574,1097],{"className":1098,"style":1091},[727],[574,1100,1102,1105,1108,1112,1116,1151,1154,1157],{"className":1101},[608],[574,1103],{"className":1104,"style":1080},[612],[574,1106,876],{"className":1107},[617,618],[574,1109,1050],{"className":1110,"style":1111},[617,618],"margin-right:0.0576em;",[574,1113,1053],{"className":1114},[1115],"mclose",[574,1117,1119],{"className":1118},[617,670],[574,1120,1122],{"className":1121},[674],[574,1123,1125],{"className":1124},[678],[574,1126,1128,1136],{"className":1127,"style":683},[682],[574,1129,1130,1133],{"style":686},[574,1131],{"className":1132,"style":691},[690],[574,1134,637],{"className":1135,"style":695},[617,618],[574,1137,1138,1141],{"style":686},[574,1139],{"className":1140,"style":691},[690],[574,1142,1144],{"className":1143,"style":705},[704],[574,1145,1147],{"className":1146,"style":710},[709],[712,1148,1149],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,1150],{"d":723},[574,1152],{"className":1153,"style":728},[727],[574,1155,774],{"className":1156},[732],[574,1158],{"className":1159,"style":728},[727],[574,1161,1163,1166],{"className":1162},[608],[574,1164],{"className":1165,"style":784},[612],[574,1167,1169],{"className":1168},[617,670],[574,1170,1172],{"className":1171},[674],[574,1173,1175],{"className":1174},[678],[574,1176,1178,1186],{"className":1177,"style":784},[682],[574,1179,1180,1183],{"style":686},[574,1181],{"className":1182,"style":691},[690],[574,1184,651],{"className":1185},[617],[574,1187,1188,1191],{"style":807},[574,1189],{"className":1190,"style":691},[690],[574,1192,1194],{"className":1193,"style":814},[704],[574,1195,1197],{"className":1196,"style":710},[709],[712,1198,1199],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,1200],{"d":723},". Dieses homogene System hat genau dann eine Lösung ",[574,1203,1205,1230],{"className":1204},[577],[574,1206,1208],{"className":1207},[581],[583,1209,1210],{"xmlns":585},[587,1211,1212,1228],{},[590,1213,1214,1220,1222],{},[633,1215,1216,1218],{"accent":604},[593,1217,637],{},[639,1219,641],{},[639,1221,645],{"mathvariant":644},[633,1223,1224,1226],{"accent":604},[649,1225,651],{},[639,1227,641],{},[597,1229,656],{"encoding":599},[574,1231,1233,1316],{"className":1232,"ariaHidden":604},[603],[574,1234,1236,1239,1274,1277,1313],{"className":1235},[608],[574,1237],{"className":1238,"style":666},[612],[574,1240,1242],{"className":1241},[617,670],[574,1243,1245],{"className":1244},[674],[574,1246,1248],{"className":1247},[678],[574,1249,1251,1259],{"className":1250,"style":683},[682],[574,1252,1253,1256],{"style":686},[574,1254],{"className":1255,"style":691},[690],[574,1257,637],{"className":1258,"style":695},[617,618],[574,1260,1261,1264],{"style":686},[574,1262],{"className":1263,"style":691},[690],[574,1265,1267],{"className":1266,"style":705},[704],[574,1268,1270],{"className":1269,"style":710},[709],[712,1271,1272],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,1273],{"d":723},[574,1275],{"className":1276,"style":728},[727],[574,1278,1280,1307,1310],{"className":1279},[732],[574,1281,1283],{"className":1282},[732],[574,1284,1286],{"className":1285},[617,739],[574,1287,1289],{"className":1288},[743],[574,1290,1292,1295,1304],{"className":1291},[747],[574,1293],{"className":1294,"style":751},[612],[574,1296,1298],{"className":1297},[755],[574,1299,1301],{"className":1300},[617],[574,1302,762],{"className":1303},[732],[574,1305],{"className":1306},[766],[574,1308],{"className":1309},[727,770],[574,1311,774],{"className":1312},[732],[574,1314],{"className":1315,"style":728},[727],[574,1317,1319,1322],{"className":1318},[608],[574,1320],{"className":1321,"style":784},[612],[574,1323,1325],{"className":1324},[617,670],[574,1326,1328],{"className":1327},[674],[574,1329,1331],{"className":1330},[678],[574,1332,1334,1342],{"className":1333,"style":784},[682],[574,1335,1336,1339],{"style":686},[574,1337],{"className":1338,"style":691},[690],[574,1340,651],{"className":1341},[617],[574,1343,1344,1347],{"style":807},[574,1345],{"className":1346,"style":691},[690],[574,1348,1350],{"className":1349,"style":814},[704],[574,1351,1353],{"className":1352,"style":710},[709],[712,1354,1355],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,1356],{"d":723},", wenn ",[574,1359,1361,1381],{"className":1360},[577],[574,1362,1364],{"className":1363},[581],[583,1365,1366],{"xmlns":585},[587,1367,1368,1378],{},[590,1369,1370,1372,1374,1376],{},[593,1371,595],{},[639,1373,1045],{},[593,1375,876],{},[593,1377,1050],{},[597,1379,1380],{"encoding":599},"A - \\lambda E",[574,1382,1384,1403],{"className":1383,"ariaHidden":604},[603],[574,1385,1387,1391,1394,1397,1400],{"className":1386},[608],[574,1388],{"className":1389,"style":1390},[612],"height:0.7667em;vertical-align:-0.0833em;",[574,1392,595],{"className":1393},[617,618],[574,1395],{"className":1396,"style":1091},[727],[574,1398,1045],{"className":1399},[1095],[574,1401],{"className":1402,"style":1091},[727],[574,1404,1406,1409,1412],{"className":1405},[608],[574,1407],{"className":1408,"style":1013},[612],[574,1410,876],{"className":1411},[617,618],[574,1413,1050],{"className":1414,"style":1111},[617,618]," nicht invertierbar ist, also wenn ",[574,1417,1419,1453],{"className":1418},[577],[574,1420,1422],{"className":1421},[581],[583,1423,1424],{"xmlns":585},[587,1425,1426,1450],{},[590,1427,1428,1431,1434,1436,1438,1440,1442,1444,1446,1448],{},[593,1429,1430],{},"det",[639,1432,1433],{},"⁡",[639,1435,1040],{"stretchy":1039},[593,1437,595],{},[639,1439,1045],{},[593,1441,876],{},[593,1443,1050],{},[639,1445,1053],{"stretchy":1039},[639,1447,774],{},[649,1449,651],{},[597,1451,1452],{"encoding":599},"\\det(A - \\lambda E) = 0",[574,1454,1456,1481,1505],{"className":1455,"ariaHidden":604},[603],[574,1457,1459,1462,1466,1469,1472,1475,1478],{"className":1458},[608],[574,1460],{"className":1461,"style":1080},[612],[574,1463,1430],{"className":1464},[1465],"mop",[574,1467,1040],{"className":1468},[1084],[574,1470,595],{"className":1471},[617,618],[574,1473],{"className":1474,"style":1091},[727],[574,1476,1045],{"className":1477},[1095],[574,1479],{"className":1480,"style":1091},[727],[574,1482,1484,1487,1490,1493,1496,1499,1502],{"className":1483},[608],[574,1485],{"className":1486,"style":1080},[612],[574,1488,876],{"className":1489},[617,618],[574,1491,1050],{"className":1492,"style":1111},[617,618],[574,1494,1053],{"className":1495},[1115],[574,1497],{"className":1498,"style":728},[727],[574,1500,774],{"className":1501},[732],[574,1503],{"className":1504,"style":728},[727],[574,1506,1508,1512],{"className":1507},[608],[574,1509],{"className":1510,"style":1511},[612],"height:0.6444em;",[574,1513,651],{"className":1514},[617],". Die linke Seite ist ein Polynom vom Grad ",[574,1517,1519,1533],{"className":1518},[577],[574,1520,1522],{"className":1521},[581],[583,1523,1524],{"xmlns":585},[587,1525,1526,1531],{},[590,1527,1528],{},[593,1529,1530],{},"n",[597,1532,1530],{"encoding":599},[574,1534,1536],{"className":1535,"ariaHidden":604},[603],[574,1537,1539,1543],{"className":1538},[608],[574,1540],{"className":1541,"style":1542},[612],"height:0.4306em;",[574,1544,1530],{"className":1545},[617,618]," in ",[574,1548,1550,1563],{"className":1549},[577],[574,1551,1553],{"className":1552},[581],[583,1554,1555],{"xmlns":585},[587,1556,1557,1561],{},[590,1558,1559],{},[593,1560,876],{},[597,1562,1003],{"encoding":599},[574,1564,1566],{"className":1565,"ariaHidden":604},[603],[574,1567,1569,1572],{"className":1568},[608],[574,1570],{"className":1571,"style":1013},[612],[574,1573,876],{"className":1574},[617,618],", das ",[569,1577,1578],{},"charakteristische Polynom"," ",[574,1581,1583,1603],{"className":1582},[577],[574,1584,1586],{"className":1585},[581],[583,1587,1588],{"xmlns":585},[587,1589,1590,1600],{},[590,1591,1592],{},[1593,1594,1595,1598],"msub",{},[593,1596,1597],{},"χ",[593,1599,595],{},[597,1601,1602],{"encoding":599},"\\chi_A",[574,1604,1606],{"className":1605,"ariaHidden":604},[603],[574,1607,1609,1613],{"className":1608},[608],[574,1610],{"className":1611,"style":1612},[612],"height:0.625em;vertical-align:-0.1944em;",[574,1614,1616,1619],{"className":1615},[617],[574,1617,1597],{"className":1618},[617,618],[574,1620,1623],{"className":1621},[1622],"msupsub",[574,1624,1627,1656],{"className":1625},[674,1626],"vlist-t2",[574,1628,1630,1651],{"className":1629},[678],[574,1631,1634],{"className":1632,"style":1633},[682],"height:0.3283em;",[574,1635,1637,1641],{"style":1636},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[574,1638],{"className":1639,"style":1640},[690],"height:2.7em;",[574,1642,1648],{"className":1643},[1644,1645,1646,1647],"sizing","reset-size6","size3","mtight",[574,1649,595],{"className":1650},[617,618,1647],[574,1652,1655],{"className":1653},[1654],"vlist-s","​",[574,1657,1659],{"className":1658},[678],[574,1660,1663],{"className":1661,"style":1662},[682],"height:0.15em;",[574,1664],{},[565,1666,1667],{},"Vorgehen:",[1669,1670,1671,1736,1768,1771],"ol",{},[1672,1673,1674,1702,1703,1706,1707,1735],"li",{},[574,1675,1677,1690],{"className":1676},[577],[574,1678,1680],{"className":1679},[581],[583,1681,1682],{"xmlns":585},[587,1683,1684,1688],{},[590,1685,1686],{},[593,1687,876],{},[597,1689,1003],{"encoding":599},[574,1691,1693],{"className":1692,"ariaHidden":604},[603],[574,1694,1696,1699],{"className":1695},[608],[574,1697],{"className":1698,"style":1013},[612],[574,1700,876],{"className":1701},[617,618]," von jedem ",[569,1704,1705],{},"Diagonaleintrag"," von ",[574,1708,1710,1723],{"className":1709},[577],[574,1711,1713],{"className":1712},[581],[583,1714,1715],{"xmlns":585},[587,1716,1717,1721],{},[590,1718,1719],{},[593,1720,595],{},[597,1722,595],{"encoding":599},[574,1724,1726],{"className":1725,"ariaHidden":604},[603],[574,1727,1729,1732],{"className":1728},[608],[574,1730],{"className":1731,"style":613},[612],[574,1733,595],{"className":1734},[617,618]," abziehen.",[1672,1737,1738,1739,1767],{},"Die Determinante berechnen und gleich ",[574,1740,1742,1755],{"className":1741},[577],[574,1743,1745],{"className":1744},[581],[583,1746,1747],{"xmlns":585},[587,1748,1749,1753],{},[590,1750,1751],{},[649,1752,651],{},[597,1754,651],{"encoding":599},[574,1756,1758],{"className":1757,"ariaHidden":604},[603],[574,1759,1761,1764],{"className":1760},[608],[574,1762],{"className":1763,"style":1511},[612],[574,1765,651],{"className":1766},[617]," setzen.",[1672,1769,1770],{},"Die Nullstellen bestimmen: Das sind die Eigenwerte.",[1672,1772,1773,1774,1938,1939,2094],{},"Für jeden Eigenwert das System ",[574,1775,1777,1814],{"className":1776},[577],[574,1778,1780],{"className":1779},[581],[583,1781,1782],{"xmlns":585},[587,1783,1784,1812],{},[590,1785,1786,1788,1790,1792,1794,1796,1798,1804,1806],{},[639,1787,1040],{"stretchy":1039},[593,1789,595],{},[639,1791,1045],{},[593,1793,876],{},[593,1795,1050],{},[639,1797,1053],{"stretchy":1039},[633,1799,1800,1802],{"accent":604},[593,1801,637],{},[639,1803,641],{},[639,1805,774],{},[633,1807,1808,1810],{"accent":604},[649,1809,651],{},[639,1811,641],{},[597,1813,1070],{"encoding":599},[574,1815,1817,1838,1897],{"className":1816,"ariaHidden":604},[603],[574,1818,1820,1823,1826,1829,1832,1835],{"className":1819},[608],[574,1821],{"className":1822,"style":1080},[612],[574,1824,1040],{"className":1825},[1084],[574,1827,595],{"className":1828},[617,618],[574,1830],{"className":1831,"style":1091},[727],[574,1833,1045],{"className":1834},[1095],[574,1836],{"className":1837,"style":1091},[727],[574,1839,1841,1844,1847,1850,1853,1888,1891,1894],{"className":1840},[608],[574,1842],{"className":1843,"style":1080},[612],[574,1845,876],{"className":1846},[617,618],[574,1848,1050],{"className":1849,"style":1111},[617,618],[574,1851,1053],{"className":1852},[1115],[574,1854,1856],{"className":1855},[617,670],[574,1857,1859],{"className":1858},[674],[574,1860,1862],{"className":1861},[678],[574,1863,1865,1873],{"className":1864,"style":683},[682],[574,1866,1867,1870],{"style":686},[574,1868],{"className":1869,"style":691},[690],[574,1871,637],{"className":1872,"style":695},[617,618],[574,1874,1875,1878],{"style":686},[574,1876],{"className":1877,"style":691},[690],[574,1879,1881],{"className":1880,"style":705},[704],[574,1882,1884],{"className":1883,"style":710},[709],[712,1885,1886],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,1887],{"d":723},[574,1889],{"className":1890,"style":728},[727],[574,1892,774],{"className":1893},[732],[574,1895],{"className":1896,"style":728},[727],[574,1898,1900,1903],{"className":1899},[608],[574,1901],{"className":1902,"style":784},[612],[574,1904,1906],{"className":1905},[617,670],[574,1907,1909],{"className":1908},[674],[574,1910,1912],{"className":1911},[678],[574,1913,1915,1923],{"className":1914,"style":784},[682],[574,1916,1917,1920],{"style":686},[574,1918],{"className":1919,"style":691},[690],[574,1921,651],{"className":1922},[617],[574,1924,1925,1928],{"style":807},[574,1926],{"className":1927,"style":691},[690],[574,1929,1931],{"className":1930,"style":814},[704],[574,1932,1934],{"className":1933,"style":710},[709],[712,1935,1936],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,1937],{"d":723}," lösen: Die Lösungen ",[574,1940,1942,1967],{"className":1941},[577],[574,1943,1945],{"className":1944},[581],[583,1946,1947],{"xmlns":585},[587,1948,1949,1965],{},[590,1950,1951,1957,1959],{},[633,1952,1953,1955],{"accent":604},[593,1954,637],{},[639,1956,641],{},[639,1958,645],{"mathvariant":644},[633,1960,1961,1963],{"accent":604},[649,1962,651],{},[639,1964,641],{},[597,1966,656],{"encoding":599},[574,1968,1970,2053],{"className":1969,"ariaHidden":604},[603],[574,1971,1973,1976,2011,2014,2050],{"className":1972},[608],[574,1974],{"className":1975,"style":666},[612],[574,1977,1979],{"className":1978},[617,670],[574,1980,1982],{"className":1981},[674],[574,1983,1985],{"className":1984},[678],[574,1986,1988,1996],{"className":1987,"style":683},[682],[574,1989,1990,1993],{"style":686},[574,1991],{"className":1992,"style":691},[690],[574,1994,637],{"className":1995,"style":695},[617,618],[574,1997,1998,2001],{"style":686},[574,1999],{"className":2000,"style":691},[690],[574,2002,2004],{"className":2003,"style":705},[704],[574,2005,2007],{"className":2006,"style":710},[709],[712,2008,2009],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,2010],{"d":723},[574,2012],{"className":2013,"style":728},[727],[574,2015,2017,2044,2047],{"className":2016},[732],[574,2018,2020],{"className":2019},[732],[574,2021,2023],{"className":2022},[617,739],[574,2024,2026],{"className":2025},[743],[574,2027,2029,2032,2041],{"className":2028},[747],[574,2030],{"className":2031,"style":751},[612],[574,2033,2035],{"className":2034},[755],[574,2036,2038],{"className":2037},[617],[574,2039,762],{"className":2040},[732],[574,2042],{"className":2043},[766],[574,2045],{"className":2046},[727,770],[574,2048,774],{"className":2049},[732],[574,2051],{"className":2052,"style":728},[727],[574,2054,2056,2059],{"className":2055},[608],[574,2057],{"className":2058,"style":784},[612],[574,2060,2062],{"className":2061},[617,670],[574,2063,2065],{"className":2064},[674],[574,2066,2068],{"className":2067},[678],[574,2069,2071,2079],{"className":2070,"style":784},[682],[574,2072,2073,2076],{"style":686},[574,2074],{"className":2075,"style":691},[690],[574,2077,651],{"className":2078},[617],[574,2080,2081,2084],{"style":807},[574,2082],{"className":2083,"style":691},[690],[574,2085,2087],{"className":2086,"style":814},[704],[574,2088,2090],{"className":2089,"style":710},[709],[712,2091,2092],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,2093],{"d":723}," sind die Eigenvektoren.",[565,2096,2097,2098,2152,2153,2384,2385,1579,2387,2436,2437,2470],{},"Für ",[574,2099,2101,2121],{"className":2100},[577],[574,2102,2104],{"className":2103},[581],[583,2105,2106],{"xmlns":585},[587,2107,2108,2118],{},[590,2109,2110,2113,2116],{},[649,2111,2112],{},"2",[639,2114,2115],{},"×",[649,2117,2112],{},[597,2119,2120],{"encoding":599},"2 \\times 2",[574,2122,2124,2143],{"className":2123,"ariaHidden":604},[603],[574,2125,2127,2131,2134,2137,2140],{"className":2126},[608],[574,2128],{"className":2129,"style":2130},[612],"height:0.7278em;vertical-align:-0.0833em;",[574,2132,2112],{"className":2133},[617],[574,2135],{"className":2136,"style":1091},[727],[574,2138,2115],{"className":2139},[1095],[574,2141],{"className":2142,"style":1091},[727],[574,2144,2146,2149],{"className":2145},[608],[574,2147],{"className":2148,"style":1511},[612],[574,2150,2112],{"className":2151},[617],"-Matrizen gilt ",[574,2154,2156,2217],{"className":2155},[577],[574,2157,2159],{"className":2158},[581],[583,2160,2161],{"xmlns":585},[587,2162,2163,2214],{},[590,2164,2165,2171,2173,2175,2177,2179,2186,2188,2191,2193,2195,2197,2199,2203,2205,2208,2210,2212],{},[1593,2166,2167,2169],{},[593,2168,1597],{},[593,2170,595],{},[639,2172,1040],{"stretchy":1039},[593,2174,876],{},[639,2176,1053],{"stretchy":1039},[639,2178,774],{},[2180,2181,2182,2184],"msup",{},[593,2183,876],{},[649,2185,2112],{},[639,2187,1045],{},[593,2189,2190],{"mathvariant":644},"Spur",[639,2192,1433],{},[639,2194,1040],{"stretchy":1039},[593,2196,595],{},[639,2198,1053],{"stretchy":1039},[2200,2201,2202],"mtext",{}," ",[593,2204,876],{},[639,2206,2207],{},"+",[593,2209,1430],{},[639,2211,1433],{},[593,2213,595],{},[597,2215,2216],{"encoding":599},"\\chi_A(\\lambda) = \\lambda^2 - \\operatorname{Spur}(A)\\,\\lambda + \\det A",[574,2218,2220,2284,2331,2369],{"className":2219,"ariaHidden":604},[603],[574,2221,2223,2226,2266,2269,2272,2275,2278,2281],{"className":2222},[608],[574,2224],{"className":2225,"style":1080},[612],[574,2227,2229,2232],{"className":2228},[617],[574,2230,1597],{"className":2231},[617,618],[574,2233,2235],{"className":2234},[1622],[574,2236,2238,2258],{"className":2237},[674,1626],[574,2239,2241,2255],{"className":2240},[678],[574,2242,2244],{"className":2243,"style":1633},[682],[574,2245,2246,2249],{"style":1636},[574,2247],{"className":2248,"style":1640},[690],[574,2250,2252],{"className":2251},[1644,1645,1646,1647],[574,2253,595],{"className":2254},[617,618,1647],[574,2256,1655],{"className":2257},[1654],[574,2259,2261],{"className":2260},[678],[574,2262,2264],{"className":2263,"style":1662},[682],[574,2265],{},[574,2267,1040],{"className":2268},[1084],[574,2270,876],{"className":2271},[617,618],[574,2273,1053],{"className":2274},[1115],[574,2276],{"className":2277,"style":728},[727],[574,2279,774],{"className":2280},[732],[574,2282],{"className":2283,"style":728},[727],[574,2285,2287,2291,2322,2325,2328],{"className":2286},[608],[574,2288],{"className":2289,"style":2290},[612],"height:0.8974em;vertical-align:-0.0833em;",[574,2292,2294,2297],{"className":2293},[617],[574,2295,876],{"className":2296},[617,618],[574,2298,2300],{"className":2299},[1622],[574,2301,2303],{"className":2302},[674],[574,2304,2306],{"className":2305},[678],[574,2307,2310],{"className":2308,"style":2309},[682],"height:0.8141em;",[574,2311,2313,2316],{"style":2312},"top:-3.063em;margin-right:0.05em;",[574,2314],{"className":2315,"style":1640},[690],[574,2317,2319],{"className":2318},[1644,1645,1646,1647],[574,2320,2112],{"className":2321},[617,1647],[574,2323],{"className":2324,"style":1091},[727],[574,2326,1045],{"className":2327},[1095],[574,2329],{"className":2330,"style":1091},[727],[574,2332,2334,2337,2344,2347,2350,2353,2357,2360,2363,2366],{"className":2333},[608],[574,2335],{"className":2336,"style":1080},[612],[574,2338,2340],{"className":2339},[1465],[574,2341,2190],{"className":2342},[617,2343],"mathrm",[574,2345,1040],{"className":2346},[1084],[574,2348,595],{"className":2349},[617,618],[574,2351,1053],{"className":2352},[1115],[574,2354],{"className":2355,"style":2356},[727],"margin-right:0.1667em;",[574,2358,876],{"className":2359},[617,618],[574,2361],{"className":2362,"style":1091},[727],[574,2364,2207],{"className":2365},[1095],[574,2367],{"className":2368,"style":1091},[727],[574,2370,2372,2375,2378,2381],{"className":2371},[608],[574,2373],{"className":2374,"style":1013},[612],[574,2376,1430],{"className":2377},[1465],[574,2379],{"className":2380,"style":2356},[727],[574,2382,595],{"className":2383},[617,618],". Dabei ist die ",[569,2386,2190],{},[574,2388,2390,2412],{"className":2389},[577],[574,2391,2393],{"className":2392},[581],[583,2394,2395],{"xmlns":585},[587,2396,2397,2409],{},[590,2398,2399,2401,2403,2405,2407],{},[593,2400,2190],{"mathvariant":644},[639,2402,1433],{},[639,2404,1040],{"stretchy":1039},[593,2406,595],{},[639,2408,1053],{"stretchy":1039},[597,2410,2411],{"encoding":599},"\\operatorname{Spur}(A)",[574,2413,2415],{"className":2414,"ariaHidden":604},[603],[574,2416,2418,2421,2427,2430,2433],{"className":2417},[608],[574,2419],{"className":2420,"style":1080},[612],[574,2422,2424],{"className":2423},[1465],[574,2425,2190],{"className":2426},[617,2343],[574,2428,1040],{"className":2429},[1084],[574,2431,595],{"className":2432},[617,618],[574,2434,1053],{"className":2435},[1115]," die Summe der Diagonaleinträge. Allgemein ist die Summe der Eigenwerte die Spur, ihr Produkt die Determinante (mit Vielfachheit, über ",[574,2438,2440,2456],{"className":2439},[577],[574,2441,2443],{"className":2442},[581],[583,2444,2445],{"xmlns":585},[587,2446,2447,2453],{},[590,2448,2449],{},[593,2450,2452],{"mathvariant":2451},"double-struck","C",[597,2454,2455],{"encoding":599},"\\mathbb{C}",[574,2457,2459],{"className":2458,"ariaHidden":604},[603],[574,2460,2462,2466],{"className":2461},[608],[574,2463],{"className":2464,"style":2465},[612],"height:0.6889em;",[574,2467,2452],{"className":2468},[617,2469],"mathbb"," gezählt). Eine reelle Matrix kann auch komplexe Eigenwerte haben, z.B. eine Drehmatrix.",[560,2472,2474],{"id":2473},"beispiele","Beispiele",[565,2476,2097,2477,2698],{},[574,2478,2480,2542],{"className":2479},[577],[574,2481,2483],{"className":2482},[581],[583,2484,2485],{"xmlns":585},[587,2486,2487,2539],{},[590,2488,2489,2491,2493],{},[593,2490,595],{},[639,2492,774],{},[590,2494,2495,2497,2537],{},[639,2496,1040],{"fence":604},[2498,2499,2503,2522],"mtable",{"rowspacing":2500,"columnalign":2501,"columnspacing":2502},"0.16em","center center","1em",[2504,2505,2506,2515],"mtr",{},[2507,2508,2509],"mtd",{},[2510,2511,2512],"mstyle",{"scriptlevel":651,"displaystyle":1039},[649,2513,2514],{},"4",[2507,2516,2517],{},[2510,2518,2519],{"scriptlevel":651,"displaystyle":1039},[649,2520,2521],{},"1",[2504,2523,2524,2530],{},[2507,2525,2526],{},[2510,2527,2528],{"scriptlevel":651,"displaystyle":1039},[649,2529,2112],{},[2507,2531,2532],{},[2510,2533,2534],{"scriptlevel":651,"displaystyle":1039},[649,2535,2536],{},"3",[639,2538,1053],{"fence":604},[597,2540,2541],{"encoding":599},"A = \\begin{pmatrix} 4 & 1 \\\\ 2 & 3 \\end{pmatrix}",[574,2543,2545,2563],{"className":2544,"ariaHidden":604},[603],[574,2546,2548,2551,2554,2557,2560],{"className":2547},[608],[574,2549],{"className":2550,"style":613},[612],[574,2552,595],{"className":2553},[617,618],[574,2555],{"className":2556,"style":728},[727],[574,2558,774],{"className":2559},[732],[574,2561],{"className":2562,"style":728},[727],[574,2564,2566,2570],{"className":2565},[608],[574,2567],{"className":2568,"style":2569},[612],"height:2.4em;vertical-align:-0.95em;",[574,2571,2574,2583,2692],{"className":2572},[2573],"minner",[574,2575,2579],{"className":2576,"style":2578},[1084,2577],"delimcenter","top:0em;",[574,2580,1040],{"className":2581},[2582,1646],"delimsizing",[574,2584,2586],{"className":2585},[617],[574,2587,2589,2639,2644,2647],{"className":2588},[2498],[574,2590,2593],{"className":2591},[2592],"col-align-c",[574,2594,2596,2630],{"className":2595},[674,1626],[574,2597,2599,2627],{"className":2598},[678],[574,2600,2603,2615],{"className":2601,"style":2602},[682],"height:1.45em;",[574,2604,2606,2609],{"style":2605},"top:-3.61em;",[574,2607],{"className":2608,"style":691},[690],[574,2610,2612],{"className":2611},[617],[574,2613,2514],{"className":2614},[617],[574,2616,2618,2621],{"style":2617},"top:-2.41em;",[574,2619],{"className":2620,"style":691},[690],[574,2622,2624],{"className":2623},[617],[574,2625,2112],{"className":2626},[617],[574,2628,1655],{"className":2629},[1654],[574,2631,2633],{"className":2632},[678],[574,2634,2637],{"className":2635,"style":2636},[682],"height:0.95em;",[574,2638],{},[574,2640],{"className":2641,"style":2643},[2642],"arraycolsep","width:0.5em;",[574,2645],{"className":2646,"style":2643},[2642],[574,2648,2650],{"className":2649},[2592],[574,2651,2653,2684],{"className":2652},[674,1626],[574,2654,2656,2681],{"className":2655},[678],[574,2657,2659,2670],{"className":2658,"style":2602},[682],[574,2660,2661,2664],{"style":2605},[574,2662],{"className":2663,"style":691},[690],[574,2665,2667],{"className":2666},[617],[574,2668,2521],{"className":2669},[617],[574,2671,2672,2675],{"style":2617},[574,2673],{"className":2674,"style":691},[690],[574,2676,2678],{"className":2677},[617],[574,2679,2536],{"className":2680},[617],[574,2682,1655],{"className":2683},[1654],[574,2685,2687],{"className":2686},[678],[574,2688,2690],{"className":2689,"style":2636},[682],[574,2691],{},[574,2693,2695],{"className":2694,"style":2578},[1115,2577],[574,2696,1053],{"className":2697},[2582,1646],":",[574,2700,2703],{"className":2701},[2702],"katex-display",[574,2704,2706,2855],{"className":2705},[577],[574,2707,2709],{"className":2708},[581],[583,2710,2712],{"xmlns":585,"display":2711},"block",[587,2713,2714,2852],{},[590,2715,2716,2718,2720,2722,2724,2726,2728,2730,2732,2734,2783,2785,2787,2789,2791,2793,2795,2797,2799,2801,2803,2805,2807,2809,2811,2817,2819,2822,2824,2826,2829,2831,2833,2835,2837,2839,2841,2843,2845,2847,2850],{},[593,2717,1430],{},[639,2719,1433],{},[639,2721,1040],{"stretchy":1039},[593,2723,595],{},[639,2725,1045],{},[593,2727,876],{},[593,2729,1050],{},[639,2731,1053],{"stretchy":1039},[639,2733,774],{},[590,2735,2736,2739,2781],{},[639,2737,2738],{"fence":604},"∣",[2498,2740,2741,2761],{"rowspacing":2500,"columnalign":2501,"columnspacing":2502},[2504,2742,2743,2755],{},[2507,2744,2745],{},[2510,2746,2747],{"scriptlevel":651,"displaystyle":1039},[590,2748,2749,2751,2753],{},[649,2750,2514],{},[639,2752,1045],{},[593,2754,876],{},[2507,2756,2757],{},[2510,2758,2759],{"scriptlevel":651,"displaystyle":1039},[649,2760,2521],{},[2504,2762,2763,2769],{},[2507,2764,2765],{},[2510,2766,2767],{"scriptlevel":651,"displaystyle":1039},[649,2768,2112],{},[2507,2770,2771],{},[2510,2772,2773],{"scriptlevel":651,"displaystyle":1039},[590,2774,2775,2777,2779],{},[649,2776,2536],{},[639,2778,1045],{},[593,2780,876],{},[639,2782,2738],{"fence":604},[639,2784,774],{},[639,2786,1040],{"stretchy":1039},[649,2788,2514],{},[639,2790,1045],{},[593,2792,876],{},[639,2794,1053],{"stretchy":1039},[639,2796,1040],{"stretchy":1039},[649,2798,2536],{},[639,2800,1045],{},[593,2802,876],{},[639,2804,1053],{"stretchy":1039},[639,2806,1045],{},[649,2808,2112],{},[639,2810,774],{},[2180,2812,2813,2815],{},[593,2814,876],{},[649,2816,2112],{},[639,2818,1045],{},[649,2820,2821],{},"7",[593,2823,876],{},[639,2825,2207],{},[649,2827,2828],{},"10",[639,2830,774],{},[639,2832,1040],{"stretchy":1039},[593,2834,876],{},[639,2836,1045],{},[649,2838,2112],{},[639,2840,1053],{"stretchy":1039},[639,2842,1040],{"stretchy":1039},[593,2844,876],{},[639,2846,1045],{},[649,2848,2849],{},"5",[639,2851,1053],{"stretchy":1039},[597,2853,2854],{"encoding":599},"\\det(A - \\lambda E) = \\begin{vmatrix} 4 - \\lambda & 1 \\\\ 2 & 3 - \\lambda \\end{vmatrix} = (4 - \\lambda)(3 - \\lambda) - 2 = \\lambda^2 - 7\\lambda + 10 = (\\lambda - 2)(\\lambda - 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Eigenwerte sind ",[574,3370,3372,3394],{"className":3371},[577],[574,3373,3375],{"className":3374},[581],[583,3376,3377],{"xmlns":585},[587,3378,3379,3391],{},[590,3380,3381,3387,3389],{},[1593,3382,3383,3385],{},[593,3384,876],{},[649,3386,2521],{},[639,3388,774],{},[649,3390,2112],{},[597,3392,3393],{"encoding":599},"\\lambda_1 = 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und ",[574,3465,3467,3489],{"className":3466},[577],[574,3468,3470],{"className":3469},[581],[583,3471,3472],{"xmlns":585},[587,3473,3474,3486],{},[590,3475,3476,3482,3484],{},[1593,3477,3478,3480],{},[593,3479,876],{},[649,3481,2112],{},[639,3483,774],{},[649,3485,2849],{},[597,3487,3488],{"encoding":599},"\\lambda_2 = 5",[574,3490,3492,3547],{"className":3491,"ariaHidden":604},[603],[574,3493,3495,3498,3538,3541,3544],{"className":3494},[608],[574,3496],{"className":3497,"style":3403},[612],[574,3499,3501,3504],{"className":3500},[617],[574,3502,876],{"className":3503},[617,618],[574,3505,3507],{"className":3506},[1622],[574,3508,3510,3530],{"className":3509},[674,1626],[574,3511,3513,3527],{"className":3512},[678],[574,3514,3516],{"className":3515,"style":3422},[682],[574,3517,3518,3521],{"style":1636},[574,3519],{"className":3520,"style":1640},[690],[574,3522,3524],{"className":3523},[1644,1645,1646,1647],[574,3525,2112],{"className":3526},[617,1647],[574,3528,1655],{"className":3529},[1654],[574,3531,3533],{"className":3532},[678],[574,3534,3536],{"className":3535,"style":1662},[682],[574,3537],{},[574,3539],{"className":3540,"style":728},[727],[574,3542,774],{"className":3543},[732],[574,3545],{"className":3546,"style":728},[727],[574,3548,3550,3553],{"className":3549},[608],[574,3551],{"className":3552,"style":1511},[612],[574,3554,2849],{"className":3555},[617],". Kontrolle: ",[574,3558,3560,3594],{"className":3559},[577],[574,3561,3563],{"className":3562},[581],[583,3564,3565],{"xmlns":585},[587,3566,3567,3591],{},[590,3568,3569,3571,3573,3575,3577,3579,3581,3583,3585,3587,3589],{},[649,3570,2112],{},[639,3572,2207],{},[649,3574,2849],{},[639,3576,774],{},[649,3578,2821],{},[639,3580,774],{},[593,3582,2190],{"mathvariant":644},[639,3584,1433],{},[639,3586,1040],{"stretchy":1039},[593,3588,595],{},[639,3590,1053],{"stretchy":1039},[597,3592,3593],{"encoding":599},"2 + 5 = 7 = \\operatorname{Spur}(A)",[574,3595,3597,3615,3633,3651],{"className":3596,"ariaHidden":604},[603],[574,3598,3600,3603,3606,3609,3612],{"className":3599},[608],[574,3601],{"className":3602,"style":2130},[612],[574,3604,2112],{"className":3605},[617],[574,3607],{"className":3608,"style":1091},[727],[574,3610,2207],{"className":3611},[1095],[574,3613],{"className":3614,"style":1091},[727],[574,3616,3618,3621,3624,3627,3630],{"className":3617},[608],[574,3619],{"className":3620,"style":1511},[612],[574,3622,2849],{"className":3623},[617],[574,3625],{"className":3626,"style":728},[727],[574,3628,774],{"className":3629},[732],[574,3631],{"className":3632,"style":728},[727],[574,3634,3636,3639,3642,3645,3648],{"className":3635},[608],[574,3637],{"className":3638,"style":1511},[612],[574,3640,2821],{"className":3641},[617],[574,3643],{"className":3644,"style":728},[727],[574,3646,774],{"className":3647},[732],[574,3649],{"className":3650,"style":728},[727],[574,3652,3654,3657,3663,3666,3669],{"className":3653},[608],[574,3655],{"className":3656,"style":1080},[612],[574,3658,3660],{"className":3659},[1465],[574,3661,2190],{"className":3662},[617,2343],[574,3664,1040],{"className":3665},[1084],[574,3667,595],{"className":3668},[617,618],[574,3670,1053],{"className":3671},[1115],[574,3673,3675,3706],{"className":3674},[577],[574,3676,3678],{"className":3677},[581],[583,3679,3680],{"xmlns":585},[587,3681,3682,3703],{},[590,3683,3684,3686,3689,3691,3693,3695,3697,3699,3701],{},[649,3685,2112],{},[639,3687,3688],{},"⋅",[649,3690,2849],{},[639,3692,774],{},[649,3694,2828],{},[639,3696,774],{},[593,3698,1430],{},[639,3700,1433],{},[593,3702,595],{},[597,3704,3705],{"encoding":599},"2 \\cdot 5 = 10 = \\det A",[574,3707,3709,3727,3745,3763],{"className":3708,"ariaHidden":604},[603],[574,3710,3712,3715,3718,3721,3724],{"className":3711},[608],[574,3713],{"className":3714,"style":1511},[612],[574,3716,2112],{"className":3717},[617],[574,3719],{"className":3720,"style":1091},[727],[574,3722,3688],{"className":3723},[1095],[574,3725],{"className":3726,"style":1091},[727],[574,3728,3730,3733,3736,3739,3742],{"className":3729},[608],[574,3731],{"className":3732,"style":1511},[612],[574,3734,2849],{"className":3735},[617],[574,3737],{"className":3738,"style":728},[727],[574,3740,774],{"className":3741},[732],[574,3743],{"className":3744,"style":728},[727],[574,3746,3748,3751,3754,3757,3760],{"className":3747},[608],[574,3749],{"className":3750,"style":1511},[612],[574,3752,2828],{"className":3753},[617],[574,3755],{"className":3756,"style":728},[727],[574,3758,774],{"className":3759},[732],[574,3761],{"className":3762,"style":728},[727],[574,3764,3766,3769,3772,3775],{"className":3765},[608],[574,3767],{"className":3768,"style":1013},[612],[574,3770,1430],{"className":3771},[1465],[574,3773],{"className":3774,"style":2356},[727],[574,3776,595],{"className":3777},[617,618],[565,3779,3780,3781,3872,3873,4266,4267,4402,4403,4521,4522,1021],{},"Eigenvektor zu ",[574,3782,3784,3805],{"className":3783},[577],[574,3785,3787],{"className":3786},[581],[583,3788,3789],{"xmlns":585},[587,3790,3791,3803],{},[590,3792,3793,3799,3801],{},[1593,3794,3795,3797],{},[593,3796,876],{},[649,3798,2112],{},[639,3800,774],{},[649,3802,2849],{},[597,3804,3488],{"encoding":599},[574,3806,3808,3863],{"className":3807,"ariaHidden":604},[603],[574,3809,3811,3814,3854,3857,3860],{"className":3810},[608],[574,3812],{"className":3813,"style":3403},[612],[574,3815,3817,3820],{"className":3816},[617],[574,3818,876],{"className":3819},[617,618],[574,3821,3823],{"className":3822},[1622],[574,3824,3826,3846],{"className":3825},[674,1626],[574,3827,3829,3843],{"className":3828},[678],[574,3830,3832],{"className":3831,"style":3422},[682],[574,3833,3834,3837],{"style":1636},[574,3835],{"className":3836,"style":1640},[690],[574,3838,3840],{"className":3839},[1644,1645,1646,1647],[574,3841,2112],{"className":3842},[617,1647],[574,3844,1655],{"className":3845},[1654],[574,3847,3849],{"className":3848},[678],[574,3850,3852],{"className":3851,"style":1662},[682],[574,3853],{},[574,3855],{"className":3856,"style":728},[727],[574,3858,774],{"className":3859},[732],[574,3861],{"className":3862,"style":728},[727],[574,3864,3866,3869],{"className":3865},[608],[574,3867],{"className":3868,"style":1511},[612],[574,3870,2849],{"className":3871},[617],": ",[574,3874,3876,3966],{"className":3875},[577],[574,3877,3879],{"className":3878},[581],[583,3880,3881],{"xmlns":585},[587,3882,3883,3963],{},[590,3884,3885,3887,3889,3891,3893,3895,3897,3903,3905,3949,3955,3957],{},[639,3886,1040],{"stretchy":1039},[593,3888,595],{},[639,3890,1045],{},[649,3892,2849],{},[593,3894,1050],{},[639,3896,1053],{"stretchy":1039},[633,3898,3899,3901],{"accent":604},[593,3900,637],{},[639,3902,641],{},[639,3904,774],{},[590,3906,3907,3909,3947],{},[639,3908,1040],{"fence":604},[2498,3910,3911,3929],{"rowspacing":2500,"columnalign":2501,"columnspacing":2502},[2504,3912,3913,3923],{},[2507,3914,3915],{},[2510,3916,3917],{"scriptlevel":651,"displaystyle":1039},[590,3918,3919,3921],{},[639,3920,1045],{},[649,3922,2521],{},[2507,3924,3925],{},[2510,3926,3927],{"scriptlevel":651,"displaystyle":1039},[649,3928,2521],{},[2504,3930,3931,3937],{},[2507,3932,3933],{},[2510,3934,3935],{"scriptlevel":651,"displaystyle":1039},[649,3936,2112],{},[2507,3938,3939],{},[2510,3940,3941],{"scriptlevel":651,"displaystyle":1039},[590,3942,3943,3945],{},[639,3944,1045],{},[649,3946,2112],{},[639,3948,1053],{"fence":604},[633,3950,3951,3953],{"accent":604},[593,3952,637],{},[639,3954,641],{},[639,3956,774],{},[633,3958,3959,3961],{"accent":604},[649,3960,651],{},[639,3962,641],{},[597,3964,3965],{"encoding":599},"(A - 5E)\\vec{v} = \\begin{pmatrix} -1 & 1 \\\\ 2 & -2 \\end{pmatrix} \\vec{v} = \\vec{0}",[574,3967,3969,3990,4049,4225],{"className":3968,"ariaHidden":604},[603],[574,3970,3972,3975,3978,3981,3984,3987],{"className":3971},[608],[574,3973],{"className":3974,"style":1080},[612],[574,3976,1040],{"className":3977},[1084],[574,3979,595],{"className":3980},[617,618],[574,3982],{"className":3983,"style":1091},[727],[574,3985,1045],{"className":3986},[1095],[574,3988],{"className":3989,"style":1091},[727],[574,3991,3993,3996,3999,4002,4005,4040,4043,4046],{"className":3992},[608],[574,3994],{"className":3995,"style":1080},[612],[574,3997,2849],{"className":3998},[617],[574,4000,1050],{"className":4001,"style":1111},[617,618],[574,4003,1053],{"className":4004},[1115],[574,4006,4008],{"className":4007},[617,670],[574,4009,4011],{"className":4010},[674],[574,4012,4014],{"className":4013},[678],[574,4015,4017,4025],{"className":4016,"style":683},[682],[574,4018,4019,4022],{"style":686},[574,4020],{"className":4021,"style":691},[690],[574,4023,637],{"className":4024,"style":695},[617,618],[574,4026,4027,4030],{"style":686},[574,4028],{"className":4029,"style":691},[690],[574,4031,4033],{"className":4032,"style":705},[704],[574,4034,4036],{"className":4035,"style":710},[709],[712,4037,4038],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,4039],{"d":723},[574,4041],{"className":4042,"style":728},[727],[574,4044,774],{"className":4045},[732],[574,4047],{"className":4048,"style":728},[727],[574,4050,4052,4055,4178,4181,4216,4219,4222],{"className":4051},[608],[574,4053],{"className":4054,"style":2569},[612],[574,4056,4058,4064,4172],{"className":4057},[2573],[574,4059,4061],{"className":4060,"style":2578},[1084,2577],[574,4062,1040],{"className":4063},[2582,1646],[574,4065,4067],{"className":4066},[617],[574,4068,4070,4118,4121,4124],{"className":4069},[2498],[574,4071,4073],{"className":4072},[2592],[574,4074,4076,4110],{"className":4075},[674,1626],[574,4077,4079,4107],{"className":4078},[678],[574,4080,4082,4096],{"className":4081,"style":2602},[682],[574,4083,4084,4087],{"style":2605},[574,4085],{"className":4086,"style":691},[690],[574,4088,4090,4093],{"className":4089},[617],[574,4091,1045],{"className":4092},[617],[574,4094,2521],{"className":4095},[617],[574,4097,4098,4101],{"style":2617},[574,4099],{"className":4100,"style":691},[690],[574,4102,4104],{"className":4103},[617],[574,4105,2112],{"className":4106},[617],[574,4108,1655],{"className":4109},[1654],[574,4111,4113],{"className":4112},[678],[574,4114,4116],{"className":4115,"style":2636},[682],[574,4117],{},[574,4119],{"className":4120,"style":2643},[2642],[574,4122],{"className":4123,"style":2643},[2642],[574,4125,4127],{"className":4126},[2592],[574,4128,4130,4164],{"className":4129},[674,1626],[574,4131,4133,4161],{"className":4132},[678],[574,4134,4136,4147],{"className":4135,"style":2602},[682],[574,4137,4138,4141],{"style":2605},[574,4139],{"className":4140,"style":691},[690],[574,4142,4144],{"className":4143},[617],[574,4145,2521],{"className":4146},[617],[574,4148,4149,4152],{"style":2617},[574,4150],{"className":4151,"style":691},[690],[574,4153,4155,4158],{"className":4154},[617],[574,4156,1045],{"className":4157},[617],[574,4159,2112],{"className":4160},[617],[574,4162,1655],{"className":4163},[1654],[574,4165,4167],{"className":4166},[678],[574,4168,4170],{"className":4169,"style":2636},[682],[574,4171],{},[574,4173,4175],{"className":4174,"style":2578},[1115,2577],[574,4176,1053],{"className":4177},[2582,1646],[574,4179],{"className":4180,"style":2356},[727],[574,4182,4184],{"className":4183},[617,670],[574,4185,4187],{"className":4186},[674],[574,4188,4190],{"className":4189},[678],[574,4191,4193,4201],{"className":4192,"style":683},[682],[574,4194,4195,4198],{"style":686},[574,4196],{"className":4197,"style":691},[690],[574,4199,637],{"className":4200,"style":695},[617,618],[574,4202,4203,4206],{"style":686},[574,4204],{"className":4205,"style":691},[690],[574,4207,4209],{"className":4208,"style":705},[704],[574,4210,4212],{"className":4211,"style":710},[709],[712,4213,4214],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,4215],{"d":723},[574,4217],{"className":4218,"style":728},[727],[574,4220,774],{"className":4221},[732],[574,4223],{"className":4224,"style":728},[727],[574,4226,4228,4231],{"className":4227},[608],[574,4229],{"className":4230,"style":784},[612],[574,4232,4234],{"className":4233},[617,670],[574,4235,4237],{"className":4236},[674],[574,4238,4240],{"className":4239},[678],[574,4241,4243,4251],{"className":4242,"style":784},[682],[574,4244,4245,4248],{"style":686},[574,4246],{"className":4247,"style":691},[690],[574,4249,651],{"className":4250},[617],[574,4252,4253,4256],{"style":807},[574,4254],{"className":4255,"style":691},[690],[574,4257,4259],{"className":4258,"style":814},[704],[574,4260,4262],{"className":4261,"style":710},[709],[712,4263,4264],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,4265],{"d":723}," liefert ",[574,4268,4270,4296],{"className":4269},[577],[574,4271,4273],{"className":4272},[581],[583,4274,4275],{"xmlns":585},[587,4276,4277,4293],{},[590,4278,4279,4285,4287],{},[1593,4280,4281,4283],{},[593,4282,637],{},[649,4284,2521],{},[639,4286,774],{},[1593,4288,4289,4291],{},[593,4290,637],{},[649,4292,2112],{},[597,4294,4295],{"encoding":599},"v_1 = v_2",[574,4297,4299,4356],{"className":4298,"ariaHidden":604},[603],[574,4300,4302,4306,4347,4350,4353],{"className":4301},[608],[574,4303],{"className":4304,"style":4305},[612],"height:0.5806em;vertical-align:-0.15em;",[574,4307,4309,4312],{"className":4308},[617],[574,4310,637],{"className":4311,"style":695},[617,618],[574,4313,4315],{"className":4314},[1622],[574,4316,4318,4339],{"className":4317},[674,1626],[574,4319,4321,4336],{"className":4320},[678],[574,4322,4324],{"className":4323,"style":3422},[682],[574,4325,4327,4330],{"style":4326},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[574,4328],{"className":4329,"style":1640},[690],[574,4331,4333],{"className":4332},[1644,1645,1646,1647],[574,4334,2521],{"className":4335},[617,1647],[574,4337,1655],{"className":4338},[1654],[574,4340,4342],{"className":4341},[678],[574,4343,4345],{"className":4344,"style":1662},[682],[574,4346],{},[574,4348],{"className":4349,"style":728},[727],[574,4351,774],{"className":4352},[732],[574,4354],{"className":4355,"style":728},[727],[574,4357,4359,4362],{"className":4358},[608],[574,4360],{"className":4361,"style":4305},[612],[574,4363,4365,4368],{"className":4364},[617],[574,4366,637],{"className":4367,"style":695},[617,618],[574,4369,4371],{"className":4370},[1622],[574,4372,4374,4394],{"className":4373},[674,1626],[574,4375,4377,4391],{"className":4376},[678],[574,4378,4380],{"className":4379,"style":3422},[682],[574,4381,4382,4385],{"style":4326},[574,4383],{"className":4384,"style":1640},[690],[574,4386,4388],{"className":4387},[1644,1645,1646,1647],[574,4389,2112],{"className":4390},[617,1647],[574,4392,1655],{"className":4393},[1654],[574,4395,4397],{"className":4396},[678],[574,4398,4400],{"className":4399,"style":1662},[682],[574,4401],{},", z.B. 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Probe: ",[574,4523,4525,4569],{"className":4524},[577],[574,4526,4528],{"className":4527},[581],[583,4529,4530],{"xmlns":585},[587,4531,4532,4566],{},[590,4533,4534,4536,4542,4544,4546,4548,4550,4552,4554,4556,4558,4560],{},[593,4535,595],{},[633,4537,4538,4540],{"accent":604},[593,4539,637],{},[639,4541,641],{},[639,4543,774],{},[639,4545,1040],{"stretchy":1039},[649,4547,2849],{},[639,4549,4429],{"separator":604},[2200,4551,4432],{},[649,4553,2849],{},[639,4555,1053],{"stretchy":1039},[639,4557,774],{},[649,4559,2849],{},[633,4561,4562,4564],{"accent":604},[593,4563,637],{},[639,4565,641],{},[597,4567,4568],{"encoding":599},"A\\vec{v} = (5,\\ 5) = 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,{},[639,4879,641],{},[597,4881,4882],{"encoding":599},"(A 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= (1,\\ -2)",[574,5359,5361,5411],{"className":5360,"ariaHidden":604},[603],[574,5362,5364,5367,5402,5405,5408],{"className":5363},[608],[574,5365],{"className":5366,"style":683},[612],[574,5368,5370],{"className":5369},[617,670],[574,5371,5373],{"className":5372},[674],[574,5374,5376],{"className":5375},[678],[574,5377,5379,5387],{"className":5378,"style":683},[682],[574,5380,5381,5384],{"style":686},[574,5382],{"className":5383,"style":691},[690],[574,5385,637],{"className":5386,"style":695},[617,618],[574,5388,5389,5392],{"style":686},[574,5390],{"className":5391,"style":691},[690],[574,5393,5395],{"className":5394,"style":705},[704],[574,5396,5398],{"className":5397,"style":710},[709],[712,5399,5400],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,5401],{"d":723},[574,5403],{"className":5404,"style":728},[727],[574,5406,774],{"className":5407},[732],[574,5409],{"className":5410,"style":728},[727],[574,5412,5414,5417,5420,5423,5426,5429,5432,5435,5438],{"className":5413},[608],[574,5415],{"className":5416,"style":1080},[612],[574,5418,1040],{"className":5419},[1084],[574,5421,2521],{"className":5422},[617],[574,5424,4429],{"className":5425},[4508],[574,5427,4432],{"className":5428},[727],[574,5430],{"className":5431,"style":2356},[727],[574,5433,1045],{"className":5434},[617],[574,5436,2112],{"className":5437},[617],[574,5439,1053],{"className":5440},[1115],[574,5442,5444,5490],{"className":5443},[577],[574,5445,5447],{"className":5446},[581],[583,5448,5449],{"xmlns":585},[587,5450,5451,5487],{},[590,5452,5453,5455,5461,5463,5465,5467,5469,5471,5473,5475,5477,5479,5481],{},[593,5454,595],{},[633,5456,5457,5459],{"accent":604},[593,5458,637],{},[639,5460,641],{},[639,5462,774],{},[639,5464,1040],{"stretchy":1039},[649,5466,2112],{},[639,5468,4429],{"separator":604},[2200,5470,4432],{},[639,5472,1045],{},[649,5474,2514],{},[639,5476,1053],{"stretchy":1039},[639,5478,774],{},[649,5480,2112],{},[633,5482,5483,5485],{"accent":604},[593,5484,637],{},[639,5486,641],{},[597,5488,5489],{"encoding":599},"A\\vec{v} = (2,\\ -4) = 2\\vec{v}",[574,5491,5493,5546,5585],{"className":5492,"ariaHidden":604},[603],[574,5494,5496,5499,5502,5537,5540,5543],{"className":5495},[608],[574,5497],{"className":5498,"style":683},[612],[574,5500,595],{"className":5501},[617,618],[574,5503,5505],{"className":5504},[617,670],[574,5506,5508],{"className":5507},[674],[574,5509,5511],{"className":5510},[678],[574,5512,5514,5522],{"className":5513,"style":683},[682],[574,5515,5516,5519],{"style":686},[574,5517],{"className":5518,"style":691},[690],[574,5520,637],{"className":5521,"style":695},[617,618],[574,5523,5524,5527],{"style":686},[574,5525],{"className":5526,"style":691},[690],[574,5528,5530],{"className":5529,"style":705},[704],[574,5531,5533],{"className":5532,"style":710},[709],[712,5534,5535],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,5536],{"d":723},[574,5538],{"className":5539,"style":728},[727],[574,5541,774],{"className":5542},[732],[574,5544],{"className":5545,"style":728},[727],[574,5547,5549,5552,5555,5558,5561,5564,5567,5570,5573,5576,5579,5582],{"className":5548},[608],[574,5550],{"className":5551,"style":1080},[612],[574,5553,1040],{"className":5554},[1084],[574,5556,2112],{"className":5557},[617],[574,5559,4429],{"className":5560},[4508],[574,5562,4432],{"className":5563},[727],[574,5565],{"className":5566,"style":2356},[727],[574,5568,1045],{"className":5569},[617],[574,5571,2514],{"className":5572},[617],[574,5574,1053],{"className":5575},[1115],[574,5577],{"className":5578,"style":728},[727],[574,5580,774],{"className":5581},[732],[574,5583],{"className":5584,"style":728},[727],[574,5586,5588,5591,5594],{"className":5587},[608],[574,5589],{"className":5590,"style":683},[612],[574,5592,2112],{"className":5593},[617],[574,5595,5597],{"className":5596},[617,670],[574,5598,5600],{"className":5599},[674],[574,5601,5603],{"className":5602},[678],[574,5604,5606,5614],{"className":5605,"style":683},[682],[574,5607,5608,5611],{"style":686},[574,5609],{"className":5610,"style":691},[690],[574,5612,637],{"className":5613,"style":695},[617,618],[574,5615,5616,5619],{"style":686},[574,5617],{"className":5618,"style":691},[690],[574,5620,5622],{"className":5621,"style":705},[704],[574,5623,5625],{"className":5624,"style":710},[709],[712,5626,5627],{"xmlns":714,"width":715,"height":716,"style":717,"viewBox":718,"preserveAspectRatio":719},[721,5628],{"d":723},[560,5630,5632],{"id":5631},"typische-fehler","Typische Fehler",[5634,5635,5636,5705,5708,5853],"ul",{},[1672,5637,5638,1706,5666,5669,5670,5704],{},[574,5639,5641,5654],{"className":5640},[577],[574,5642,5644],{"className":5643},[581],[583,5645,5646],{"xmlns":585},[587,5647,5648,5652],{},[590,5649,5650],{},[593,5651,876],{},[597,5653,1003],{"encoding":599},[574,5655,5657],{"className":5656,"ariaHidden":604},[603],[574,5658,5660,5663],{"className":5659},[608],[574,5661],{"className":5662,"style":1013},[612],[574,5664,876],{"className":5665},[617,618],[569,5667,5668],{},"allen"," Einträgen abziehen. Abgezogen wird nur auf der Diagonalen, denn ",[574,5671,5673,5689],{"className":5672},[577],[574,5674,5676],{"className":5675},[581],[583,5677,5678],{"xmlns":585},[587,5679,5680,5686],{},[590,5681,5682,5684],{},[593,5683,876],{},[593,5685,1050],{},[597,5687,5688],{"encoding":599},"\\lambda E",[574,5690,5692],{"className":5691,"ariaHidden":604},[603],[574,5693,5695,5698,5701],{"className":5694},[608],[574,5696],{"className":5697,"style":1013},[612],[574,5699,876],{"className":5700},[617,618],[574,5702,1050],{"className":5703,"style":1111},[617,618]," hat außerhalb der Diagonalen Nullen.",[1672,5706,5707],{},"Den Nullvektor als Eigenvektor angeben. Eigenvektoren sind per Definition vom Nullvektor verschieden.",[1672,5709,5710,5778,5779,5852],{},[574,5711,5713,5739],{"className":5712},[577],[574,5714,5716],{"className":5715},[581],[583,5717,5718],{"xmlns":585},[587,5719,5720,5736],{},[590,5721,5722,5724,5726,5728,5730,5732,5734],{},[593,5723,1430],{},[639,5725,1433],{},[639,5727,1040],{"stretchy":1039},[593,5729,595],{},[639,5731,1053],{"stretchy":1039},[639,5733,1045],{},[593,5735,876],{},[597,5737,5738],{"encoding":599},"\\det(A) - \\lambda",[574,5740,5742,5769],{"className":5741,"ariaHidden":604},[603],[574,5743,5745,5748,5751,5754,5757,5760,5763,5766],{"className":5744},[608],[574,5746],{"className":5747,"style":1080},[612],[574,5749,1430],{"className":5750},[1465],[574,5752,1040],{"className":5753},[1084],[574,5755,595],{"className":5756},[617,618],[574,5758,1053],{"className":5759},[1115],[574,5761],{"className":5762,"style":1091},[727],[574,5764,1045],{"className":5765},[1095],[574,5767],{"className":5768,"style":1091},[727],[574,5770,5772,5775],{"className":5771},[608],[574,5773],{"className":5774,"style":1013},[612],[574,5776,876],{"className":5777},[617,618]," statt ",[574,5780,5782,5810],{"className":5781},[577],[574,5783,5785],{"className":5784},[581],[583,5786,5787],{"xmlns":585},[587,5788,5789,5807],{},[590,5790,5791,5793,5795,5797,5799,5801,5803,5805],{},[593,5792,1430],{},[639,5794,1433],{},[639,5796,1040],{"stretchy":1039},[593,5798,595],{},[639,5800,1045],{},[593,5802,876],{},[593,5804,1050],{},[639,5806,1053],{"stretchy":1039},[597,5808,5809],{"encoding":599},"\\det(A - \\lambda E)",[574,5811,5813,5837],{"className":5812,"ariaHidden":604},[603],[574,5814,5816,5819,5822,5825,5828,5831,5834],{"className":5815},[608],[574,5817],{"className":5818,"style":1080},[612],[574,5820,1430],{"className":5821},[1465],[574,5823,1040],{"className":5824},[1084],[574,5826,595],{"className":5827},[617,618],[574,5829],{"className":5830,"style":1091},[727],[574,5832,1045],{"className":5833},[1095],[574,5835],{"className":5836,"style":1091},[727],[574,5838,5840,5843,5846,5849],{"className":5839},[608],[574,5841],{"className":5842,"style":1080},[612],[574,5844,876],{"className":5845},[617,618],[574,5847,1050],{"className":5848,"style":1111},[617,618],[574,5850,1053],{"className":5851},[1115]," rechnen.",[1672,5854,5855,5856,6038,6039,6120],{},"Erwarten, dass jede reelle Matrix reelle Eigenwerte hat. ",[574,5857,5859,5909],{"className":5858},[577],[574,5860,5862],{"className":5861},[581],[583,5863,5864],{"xmlns":585},[587,5865,5866,5906],{},[590,5867,5868,5870,5904],{},[639,5869,1040],{"fence":604},[2498,5871,5872,5890],{"rowspacing":2500,"columnalign":2501,"columnspacing":2502},[2504,5873,5874,5880],{},[2507,5875,5876],{},[2510,5877,5878],{"scriptlevel":651,"displaystyle":1039},[649,5879,651],{},[2507,5881,5882],{},[2510,5883,5884],{"scriptlevel":651,"displaystyle":1039},[590,5885,5886,5888],{},[639,5887,1045],{},[649,5889,2521],{},[2504,5891,5892,5898],{},[2507,5893,5894],{},[2510,5895,5896],{"scriptlevel":651,"displaystyle":1039},[649,5897,2521],{},[2507,5899,5900],{},[2510,5901,5902],{"scriptlevel":651,"displaystyle":1039},[649,5903,651],{},[639,5905,1053],{"fence":604},[597,5907,5908],{"encoding":599},"\\begin{pmatrix} 0 & -1 \\\\ 1 & 0 \\end{pmatrix}",[574,5910,5912],{"className":5911,"ariaHidden":604},[603],[574,5913,5915,5918],{"className":5914},[608],[574,5916],{"className":5917,"style":2569},[612],[574,5919,5921,5927,6032],{"className":5920},[2573],[574,5922,5924],{"className":5923,"style":2578},[1084,2577],[574,5925,1040],{"className":5926},[2582,1646],[574,5928,5930],{"className":5929},[617],[574,5931,5933,5978,5981,5984],{"className":5932},[2498],[574,5934,5936],{"className":5935},[2592],[574,5937,5939,5970],{"className":5938},[674,1626],[574,5940,5942,5967],{"className":5941},[678],[574,5943,5945,5956],{"className":5944,"style":2602},[682],[574,5946,5947,5950],{"style":2605},[574,5948],{"className":5949,"style":691},[690],[574,5951,5953],{"className":5952},[617],[574,5954,651],{"className":5955},[617],[574,5957,5958,5961],{"style":2617},[574,5959],{"className":5960,"style":691},[690],[574,5962,5964],{"className":5963},[617],[574,5965,2521],{"className":5966},[617],[574,5968,1655],{"className":5969},[1654],[574,5971,5973],{"className":5972},[678],[574,5974,5976],{"className":5975,"style":2636},[682],[574,5977],{},[574,5979],{"className":5980,"style":2643},[2642],[574,5982],{"className":5983,"style":2643},[2642],[574,5985,5987],{"className":5986},[2592],[574,5988,5990,6024],{"className":5989},[674,1626],[574,5991,5993,6021],{"className":5992},[678],[574,5994,5996,6010],{"className":5995,"style":2602},[682],[574,5997,5998,6001],{"style":2605},[574,5999],{"className":6000,"style":691},[690],[574,6002,6004,6007],{"className":6003},[617],[574,6005,1045],{"className":6006},[617],[574,6008,2521],{"className":6009},[617],[574,6011,6012,6015],{"style":2617},[574,6013],{"className":6014,"style":691},[690],[574,6016,6018],{"className":6017},[617],[574,6019,651],{"className":6020},[617],[574,6022,1655],{"className":6023},[1654],[574,6025,6027],{"className":6026},[678],[574,6028,6030],{"className":6029,"style":2636},[682],[574,6031],{},[574,6033,6035],{"className":6034,"style":2578},[1115,2577],[574,6036,1053],{"className":6037},[2582,1646]," hat das Polynom ",[574,6040,6042,6064],{"className":6041},[577],[574,6043,6045],{"className":6044},[581],[583,6046,6047],{"xmlns":585},[587,6048,6049,6061],{},[590,6050,6051,6057,6059],{},[2180,6052,6053,6055],{},[593,6054,876],{},[649,6056,2112],{},[639,6058,2207],{},[649,6060,2521],{},[597,6062,6063],{"encoding":599},"\\lambda^2 + 1",[574,6065,6067,6111],{"className":6066,"ariaHidden":604},[603],[574,6068,6070,6073,6102,6105,6108],{"className":6069},[608],[574,6071],{"className":6072,"style":2290},[612],[574,6074,6076,6079],{"className":6075},[617],[574,6077,876],{"className":6078},[617,618],[574,6080,6082],{"className":6081},[1622],[574,6083,6085],{"className":6084},[674],[574,6086,6088],{"className":6087},[678],[574,6089,6091],{"className":6090,"style":2309},[682],[574,6092,6093,6096],{"style":2312},[574,6094],{"className":6095,"style":1640},[690],[574,6097,6099],{"className":6098},[1644,1645,1646,1647],[574,6100,2112],{"className":6101},[617,1647],[574,6103],{"className":6104,"style":1091},[727],[574,6106,2207],{"className":6107},[1095],[574,6109],{"className":6110,"style":1091},[727],[574,6112,6114,6117],{"className":6113},[608],[574,6115],{"className":6116,"style":1511},[612],[574,6118,2521],{"className":6119},[617]," und keine reellen Eigenwerte.",{"title":6122,"searchDepth":6123,"depth":6123,"links":6124},"",2,[6125,6126,6127],{"id":562,"depth":6123,"text":563},{"id":2473,"depth":6123,"text":2474},{"id":5631,"depth":6123,"text":5632},[6129,6132,6135,6137,6139,6142,6145,6147,6150,6153,6156,6159],{"lhs":6130,"rhs":6131},"det([[a11 - x, a12], [a21, a22 - x]])","x^2 - (a11 + a22)*x + (a11*a22 - a12*a21)",{"lhs":6133,"rhs":6134},"(4 - x)*(3 - x) - 1*2","x^2 - 7*x + 10",{"lhs":6134,"rhs":6136},"(x - 2)*(x - 5)",{"lhs":6134,"rhs":651,"where":6138},{"x":6123},{"lhs":6134,"rhs":651,"where":6140},{"x":6141},5,{"lhs":6143,"rhs":6144},"4*1 + 1*1","5*1",{"lhs":6146,"rhs":6144},"2*1 + 3*1",{"lhs":6148,"rhs":6149},"4*1 + 1*(-2)","2*1",{"lhs":6151,"rhs":6152},"2*1 + 3*(-2)","2*(-2)",{"lhs":6154,"rhs":6155},"2 + 5","4 + 3",{"lhs":6157,"rhs":6158},"2 * 5","4*3 - 1*2",{"lhs":6160,"rhs":6161},"det([[0 - x, -1], [1, 0 - x]])","x^2 + 1","A \\in \\mathbb{R}^{n \\times n}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\in \\mathbb{R}^{n \\times n}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\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:0.7713em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\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 mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","characteristic-polynomial","\\chi_A(\\lambda) = \\det(A - \\lambda E) = 0","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>χ\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>λ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>λ\u003C\u002Fmi>\u003Cmi>E\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\chi_A(\\lambda) = \\det(A - \\lambda E) = 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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">χ\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3283em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">λ\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=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\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 mathnormal\">λ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Feigenwerte-charakteristisches-polynom",[],[6175,6176,6177,6178],"determinant-2x2","determinant-3x3","eigenvalue-properties","diagonalization",{"title":548,"description":6122},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Feigenwerte-charakteristisches-polynom","Die Eigenwerte einer Matrix sind die Nullstellen ihres charakteristischen Polynoms det(A − λE).",[6183,6184,6185,6186,6187],"eigenwert","eigenvektor","charakteristisches polynom","determinante","matrix",[6189,6192,6195,6198],{"symbol":595,"meaning":6190,"symbolHtml":6191},"quadratische Matrix","\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 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style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":1003,"meaning":6196,"symbolHtml":6197},"Eigenwert von A, eine Nullstelle des charakteristischen Polynoms","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>λ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lambda\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=\"mord mathnormal\">λ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":6199,"meaning":6200,"symbolHtml":6201},"\\chi_A(\\lambda)","charakteristisches Polynom von A, ein Polynom vom Grad n in λ","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>χ\u003C\u002Fmi>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>λ\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\chi_A(\\lambda)\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\">\u003Cspan class=\"mord 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