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D",[569,838,840,896],{"className":839,"ariaHidden":599},[598],[569,841,843,846,881,884,887,890,893],{"className":842},[603],[569,844],{"className":845,"style":750},[607],[569,847,849,852],{"className":848},[612],[569,850,633],{"className":851,"style":648},[612,613],[569,853,855],{"className":854},[766],[569,856,858],{"className":857},[770],[569,859,861],{"className":860},[774],[569,862,864],{"className":863,"style":750},[778],[569,865,866,869],{"style":781},[569,867],{"className":868,"style":786},[785],[569,870,872],{"className":871},[790,791,792,793],[569,873,875,878],{"className":874},[612,793],[569,876,712],{"className":877},[612,793],[569,879,716],{"className":880},[612,793],[569,882,590],{"className":883},[612,613],[569,885,633],{"className":886,"style":648},[612,613],[569,888],{"className":889,"style":736},[735],[569,891,698],{"className":892},[740],[569,894],{"className":895,"style":736},[735],[569,897,899,902],{"className":898},[603],[569,900],{"className":901,"style":608},[607],[569,903,664],{"className":904,"style":679},[612,613],". Die Spalten von ",[569,907,909,922],{"className":908},[572],[569,910,912],{"className":911},[576],[578,913,914],{"xmlns":580},[582,915,916,920],{},[585,917,918],{},[588,919,633],{},[592,921,633],{"encoding":594},[569,923,925],{"className":924,"ariaHidden":599},[598],[569,926,928,931],{"className":927},[603],[569,929],{"className":930,"style":608},[607],[569,932,633],{"className":933,"style":648},[612,613]," sind dann Eigenvektoren, die Diagonale von ",[569,936,938,951],{"className":937},[572],[569,939,941],{"className":940},[576],[578,942,943],{"xmlns":580},[582,944,945,949],{},[585,946,947],{},[588,948,664],{},[592,950,664],{"encoding":594},[569,952,954],{"className":953,"ariaHidden":599},[598],[569,955,957,960],{"className":956},[603],[569,958],{"className":959,"style":608},[607],[569,961,664],{"className":962,"style":679},[612,613]," enthält die zugehörigen Eigenwerte in derselben Reihenfolge. Geometrisch: In der Basis aus Eigenvektoren wirkt ",[569,965,967,980],{"className":966},[572],[569,968,970],{"className":969},[576],[578,971,972],{"xmlns":580},[582,973,974,978],{},[585,975,976],{},[588,977,590],{},[592,979,590],{"encoding":594},[569,981,983],{"className":982,"ariaHidden":599},[598],[569,984,986,989],{"className":985},[603],[569,987],{"className":988,"style":608},[607],[569,990,590],{"className":991},[612,613]," als reine Streckung entlang der Achsen.",[565,994,995],{},"Vorgehen:",[997,998,999,1090,1173],"ol",{},[1000,1001,1002,1003,1089],"li",{},"Eigenwerte als Nullstellen von ",[569,1004,1006,1041],{"className":1005},[572],[569,1007,1009],{"className":1008},[576],[578,1010,1011],{"xmlns":580},[582,1012,1013,1038],{},[585,1014,1015,1018,1021,1025,1027,1029,1032,1035],{},[588,1016,1017],{},"det",[696,1019,1020],{},"⁡",[696,1022,1024],{"stretchy":1023},"false","(",[588,1026,590],{},[696,1028,712],{},[588,1030,1031],{},"λ",[588,1033,1034],{},"E",[696,1036,1037],{"stretchy":1023},")",[592,1039,1040],{"encoding":594},"\\det(A - \\lambda E)",[569,1042,1044,1073],{"className":1043,"ariaHidden":599},[598],[569,1045,1047,1051,1055,1059,1062,1066,1070],{"className":1046},[603],[569,1048],{"className":1049,"style":1050},[607],"height:1em;vertical-align:-0.25em;",[569,1052,1017],{"className":1053},[1054],"mop",[569,1056,1024],{"className":1057},[1058],"mopen",[569,1060,590],{"className":1061},[612,613],[569,1063],{"className":1064,"style":1065},[735],"margin-right:0.2222em;",[569,1067,712],{"className":1068},[1069],"mbin",[569,1071],{"className":1072,"style":1065},[735],[569,1074,1076,1079,1082,1085],{"className":1075},[603],[569,1077],{"className":1078,"style":1050},[607],[569,1080,1031],{"className":1081},[612,613],[569,1083,1034],{"className":1084,"style":648},[612,613],[569,1086,1037],{"className":1087},[1088],"mclose"," bestimmen.",[1000,1091,1092,1093,1172],{},"Zu jedem Eigenwert eine Basis des Eigenraums ",[569,1094,1096,1126],{"className":1095},[572],[569,1097,1099],{"className":1098},[576],[578,1100,1101],{"xmlns":580},[582,1102,1103,1123],{},[585,1104,1105,1109,1111,1113,1115,1117,1119,1121],{},[588,1106,1108],{"mathvariant":1107},"normal","Kern",[696,1110,1020],{},[696,1112,1024],{"stretchy":1023},[588,1114,590],{},[696,1116,712],{},[588,1118,1031],{},[588,1120,1034],{},[696,1122,1037],{"stretchy":1023},[592,1124,1125],{"encoding":594},"\\operatorname{Kern}(A - \\lambda E)",[569,1127,1129,1157],{"className":1128,"ariaHidden":599},[598],[569,1130,1132,1135,1142,1145,1148,1151,1154],{"className":1131},[603],[569,1133],{"className":1134,"style":1050},[607],[569,1136,1138],{"className":1137},[1054],[569,1139,1108],{"className":1140},[612,1141],"mathrm",[569,1143,1024],{"className":1144},[1058],[569,1146,590],{"className":1147},[612,613],[569,1149],{"className":1150,"style":1065},[735],[569,1152,712],{"className":1153},[1069],[569,1155],{"className":1156,"style":1065},[735],[569,1158,1160,1163,1166,1169],{"className":1159},[603],[569,1161],{"className":1162,"style":1050},[607],[569,1164,1031],{"className":1165},[612,613],[569,1167,1034],{"className":1168,"style":648},[612,613],[569,1170,1037],{"className":1171},[1088]," berechnen.",[1000,1174,1175,1176,1206,1207,1235,1236,1264],{},"Sind es insgesamt ",[569,1177,1179,1193],{"className":1178},[572],[569,1180,1182],{"className":1181},[576],[578,1183,1184],{"xmlns":580},[582,1185,1186,1191],{},[585,1187,1188],{},[588,1189,1190],{},"n",[592,1192,1190],{"encoding":594},[569,1194,1196],{"className":1195,"ariaHidden":599},[598],[569,1197,1199,1203],{"className":1198},[603],[569,1200],{"className":1201,"style":1202},[607],"height:0.4306em;",[569,1204,1190],{"className":1205},[612,613]," Eigenvektoren, diese als Spalten in ",[569,1208,1210,1223],{"className":1209},[572],[569,1211,1213],{"className":1212},[576],[578,1214,1215],{"xmlns":580},[582,1216,1217,1221],{},[585,1218,1219],{},[588,1220,633],{},[592,1222,633],{"encoding":594},[569,1224,1226],{"className":1225,"ariaHidden":599},[598],[569,1227,1229,1232],{"className":1228},[603],[569,1230],{"className":1231,"style":608},[607],[569,1233,633],{"className":1234,"style":648},[612,613]," schreiben. Sonst ist ",[569,1237,1239,1252],{"className":1238},[572],[569,1240,1242],{"className":1241},[576],[578,1243,1244],{"xmlns":580},[582,1245,1246,1250],{},[585,1247,1248],{},[588,1249,590],{},[592,1251,590],{"encoding":594},[569,1253,1255],{"className":1254,"ariaHidden":599},[598],[569,1256,1258,1261],{"className":1257},[603],[569,1259],{"className":1260,"style":608},[607],[569,1262,590],{"className":1263},[612,613]," nicht diagonalisierbar.",[565,1266,1267],{},"Kriterien:",[1269,1270,1271,1335,1346],"ul",{},[1000,1272,1273,1301,1302,1305,1306,1334],{},[569,1274,1276,1289],{"className":1275},[572],[569,1277,1279],{"className":1278},[576],[578,1280,1281],{"xmlns":580},[582,1282,1283,1287],{},[585,1284,1285],{},[588,1286,1190],{},[592,1288,1190],{"encoding":594},[569,1290,1292],{"className":1291,"ariaHidden":599},[598],[569,1293,1295,1298],{"className":1294},[603],[569,1296],{"className":1297,"style":1202},[607],[569,1299,1190],{"className":1300},[612,613]," ",[616,1303,1304],{},"verschiedene"," Eigenwerte: ",[569,1307,1309,1322],{"className":1308},[572],[569,1310,1312],{"className":1311},[576],[578,1313,1314],{"xmlns":580},[582,1315,1316,1320],{},[585,1317,1318],{},[588,1319,590],{},[592,1321,590],{"encoding":594},[569,1323,1325],{"className":1324,"ariaHidden":599},[598],[569,1326,1328,1331],{"className":1327},[603],[569,1329],{"className":1330,"style":608},[607],[569,1332,590],{"className":1333},[612,613]," ist diagonalisierbar.",[1000,1336,1337,1338,1341,1342,1345],{},"Allgemein: Das charakteristische Polynom zerfällt in Linearfaktoren, und für jeden Eigenwert ist die ",[616,1339,1340],{},"geometrische Vielfachheit"," (Dimension des Eigenraums) gleich der ",[616,1343,1344],{},"algebraischen"," (Vielfachheit als Nullstelle).",[1000,1347,1348,1349,1377],{},"Jede reelle symmetrische Matrix ist diagonalisierbar, sogar mit orthogonalem ",[569,1350,1352,1365],{"className":1351},[572],[569,1353,1355],{"className":1354},[576],[578,1356,1357],{"xmlns":580},[582,1358,1359,1363],{},[585,1360,1361],{},[588,1362,633],{},[592,1364,633],{"encoding":594},[569,1366,1368],{"className":1367,"ariaHidden":599},[598],[569,1369,1371,1374],{"className":1370},[603],[569,1372],{"className":1373,"style":608},[607],[569,1375,633],{"className":1376,"style":648},[612,613],".",[565,1379,1380,1381,1384,1385,1549,1550,1609],{},"Hauptanwendung sind ",[616,1382,1383],{},"Matrixpotenzen",": ",[569,1386,1388,1427],{"className":1387},[572],[569,1389,1391],{"className":1390},[576],[578,1392,1393],{"xmlns":580},[582,1394,1395,1424],{},[585,1396,1397,1404,1406,1408,1414],{},[704,1398,1399,1401],{},[588,1400,590],{},[588,1402,1403],{},"k",[696,1405,698],{},[588,1407,633],{},[704,1409,1410,1412],{},[588,1411,664],{},[588,1413,1403],{},[704,1415,1416,1418],{},[588,1417,633],{},[585,1419,1420,1422],{},[696,1421,712],{},[714,1423,716],{},[592,1425,1426],{"encoding":594},"A^k = S D^k S^{-1}",[569,1428,1430,1476],{"className":1429,"ariaHidden":599},[598],[569,1431,1433,1437,1467,1470,1473],{"className":1432},[603],[569,1434],{"className":1435,"style":1436},[607],"height:0.8491em;",[569,1438,1440,1443],{"className":1439},[612],[569,1441,590],{"className":1442},[612,613],[569,1444,1446],{"className":1445},[766],[569,1447,1449],{"className":1448},[770],[569,1450,1452],{"className":1451},[774],[569,1453,1455],{"className":1454,"style":1436},[778],[569,1456,1457,1460],{"style":781},[569,1458],{"className":1459,"style":786},[785],[569,1461,1463],{"className":1462},[790,791,792,793],[569,1464,1403],{"className":1465,"style":1466},[612,613,793],"margin-right:0.0315em;",[569,1468],{"className":1469,"style":736},[735],[569,1471,698],{"className":1472},[740],[569,1474],{"className":1475,"style":736},[735],[569,1477,1479,1482,1485,1514],{"className":1478},[603],[569,1480],{"className":1481,"style":1436},[607],[569,1483,633],{"className":1484,"style":648},[612,613],[569,1486,1488,1491],{"className":1487},[612],[569,1489,664],{"className":1490,"style":679},[612,613],[569,1492,1494],{"className":1493},[766],[569,1495,1497],{"className":1496},[770],[569,1498,1500],{"className":1499},[774],[569,1501,1503],{"className":1502,"style":1436},[778],[569,1504,1505,1508],{"style":781},[569,1506],{"className":1507,"style":786},[785],[569,1509,1511],{"className":1510},[790,791,792,793],[569,1512,1403],{"className":1513,"style":1466},[612,613,793],[569,1515,1517,1520],{"className":1516},[612],[569,1518,633],{"className":1519,"style":648},[612,613],[569,1521,1523],{"className":1522},[766],[569,1524,1526],{"className":1525},[770],[569,1527,1529],{"className":1528},[774],[569,1530,1532],{"className":1531,"style":750},[778],[569,1533,1534,1537],{"style":781},[569,1535],{"className":1536,"style":786},[785],[569,1538,1540],{"className":1539},[790,791,792,793],[569,1541,1543,1546],{"className":1542},[612,793],[569,1544,712],{"className":1545},[612,793],[569,1547,716],{"className":1548},[612,793],", und ",[569,1551,1553,1571],{"className":1552},[572],[569,1554,1556],{"className":1555},[576],[578,1557,1558],{"xmlns":580},[582,1559,1560,1568],{},[585,1561,1562],{},[704,1563,1564,1566],{},[588,1565,664],{},[588,1567,1403],{},[592,1569,1570],{"encoding":594},"D^k",[569,1572,1574],{"className":1573,"ariaHidden":599},[598],[569,1575,1577,1580],{"className":1576},[603],[569,1578],{"className":1579,"style":1436},[607],[569,1581,1583,1586],{"className":1582},[612],[569,1584,664],{"className":1585,"style":679},[612,613],[569,1587,1589],{"className":1588},[766],[569,1590,1592],{"className":1591},[770],[569,1593,1595],{"className":1594},[774],[569,1596,1598],{"className":1597,"style":1436},[778],[569,1599,1600,1603],{"style":781},[569,1601],{"className":1602,"style":786},[785],[569,1604,1606],{"className":1605},[790,791,792,793],[569,1607,1403],{"className":1608,"style":1466},[612,613,793]," erhält man durch Potenzieren der Diagonaleinträge.",[560,1611,1613],{"id":1612},"beispiele","Beispiele",[565,1615,1616,1842,1843,1941,1942,2130,2131,1941,2224,2380],{},[569,1617,1619,1682],{"className":1618},[572],[569,1620,1622],{"className":1621},[576],[578,1623,1624],{"xmlns":580},[582,1625,1626,1679],{},[585,1627,1628,1630,1632],{},[588,1629,590],{},[696,1631,698],{},[585,1633,1634,1636,1677],{},[696,1635,1024],{"fence":599},[1637,1638,1642,1661],"mtable",{"rowspacing":1639,"columnalign":1640,"columnspacing":1641},"0.16em","center center","1em",[1643,1644,1645,1655],"mtr",{},[1646,1647,1648],"mtd",{},[1649,1650,1652],"mstyle",{"scriptlevel":1651,"displaystyle":1023},"0",[714,1653,1654],{},"4",[1646,1656,1657],{},[1649,1658,1659],{"scriptlevel":1651,"displaystyle":1023},[714,1660,716],{},[1643,1662,1663,1670],{},[1646,1664,1665],{},[1649,1666,1667],{"scriptlevel":1651,"displaystyle":1023},[714,1668,1669],{},"2",[1646,1671,1672],{},[1649,1673,1674],{"scriptlevel":1651,"displaystyle":1023},[714,1675,1676],{},"3",[696,1678,1037],{"fence":599},[592,1680,1681],{"encoding":594},"A = \\begin{pmatrix} 4 & 1 \\\\ 2 & 3 \\end{pmatrix}",[569,1683,1685,1703],{"className":1684,"ariaHidden":599},[598],[569,1686,1688,1691,1694,1697,1700],{"className":1687},[603],[569,1689],{"className":1690,"style":608},[607],[569,1692,590],{"className":1693},[612,613],[569,1695],{"className":1696,"style":736},[735],[569,1698,698],{"className":1699},[740],[569,1701],{"className":1702,"style":736},[735],[569,1704,1706,1710],{"className":1705},[603],[569,1707],{"className":1708,"style":1709},[607],"height:2.4em;vertical-align:-0.95em;",[569,1711,1714,1723,1836],{"className":1712},[1713],"minner",[569,1715,1719],{"className":1716,"style":1718},[1058,1717],"delimcenter","top:0em;",[569,1720,1024],{"className":1721},[1722,792],"delimsizing",[569,1724,1726],{"className":1725},[612],[569,1727,1729,1783,1788,1791],{"className":1728},[1637],[569,1730,1733],{"className":1731},[1732],"col-align-c",[569,1734,1737,1774],{"className":1735},[770,1736],"vlist-t2",[569,1738,1740,1769],{"className":1739},[774],[569,1741,1744,1757],{"className":1742,"style":1743},[778],"height:1.45em;",[569,1745,1747,1751],{"style":1746},"top:-3.61em;",[569,1748],{"className":1749,"style":1750},[785],"height:3em;",[569,1752,1754],{"className":1753},[612],[569,1755,1654],{"className":1756},[612],[569,1758,1760,1763],{"style":1759},"top:-2.41em;",[569,1761],{"className":1762,"style":1750},[785],[569,1764,1766],{"className":1765},[612],[569,1767,1669],{"className":1768},[612],[569,1770,1773],{"className":1771},[1772],"vlist-s","​",[569,1775,1777],{"className":1776},[774],[569,1778,1781],{"className":1779,"style":1780},[778],"height:0.95em;",[569,1782],{},[569,1784],{"className":1785,"style":1787},[1786],"arraycolsep","width:0.5em;",[569,1789],{"className":1790,"style":1787},[1786],[569,1792,1794],{"className":1793},[1732],[569,1795,1797,1828],{"className":1796},[770,1736],[569,1798,1800,1825],{"className":1799},[774],[569,1801,1803,1814],{"className":1802,"style":1743},[778],[569,1804,1805,1808],{"style":1746},[569,1806],{"className":1807,"style":1750},[785],[569,1809,1811],{"className":1810},[612],[569,1812,716],{"className":1813},[612],[569,1815,1816,1819],{"style":1759},[569,1817],{"className":1818,"style":1750},[785],[569,1820,1822],{"className":1821},[612],[569,1823,1676],{"className":1824},[612],[569,1826,1773],{"className":1827},[1772],[569,1829,1831],{"className":1830},[774],[569,1832,1834],{"className":1833,"style":1780},[778],[569,1835],{},[569,1837,1839],{"className":1838,"style":1718},[1088,1717],[569,1840,1037],{"className":1841},[1722,792]," hat die Eigenwerte ",[569,1844,1846,1869],{"className":1845},[572],[569,1847,1849],{"className":1848},[576],[578,1850,1851],{"xmlns":580},[582,1852,1853,1866],{},[585,1854,1855,1862,1864],{},[1856,1857,1858,1860],"msub",{},[588,1859,1031],{},[714,1861,716],{},[696,1863,698],{},[714,1865,1669],{},[592,1867,1868],{"encoding":594},"\\lambda_1 = 2",[569,1870,1872,1931],{"className":1871,"ariaHidden":599},[598],[569,1873,1875,1879,1922,1925,1928],{"className":1874},[603],[569,1876],{"className":1877,"style":1878},[607],"height:0.8444em;vertical-align:-0.15em;",[569,1880,1882,1885],{"className":1881},[612],[569,1883,1031],{"className":1884},[612,613],[569,1886,1888],{"className":1887},[766],[569,1889,1891,1913],{"className":1890},[770,1736],[569,1892,1894,1910],{"className":1893},[774],[569,1895,1898],{"className":1896,"style":1897},[778],"height:0.3011em;",[569,1899,1901,1904],{"style":1900},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[569,1902],{"className":1903,"style":786},[785],[569,1905,1907],{"className":1906},[790,791,792,793],[569,1908,716],{"className":1909},[612,793],[569,1911,1773],{"className":1912},[1772],[569,1914,1916],{"className":1915},[774],[569,1917,1920],{"className":1918,"style":1919},[778],"height:0.15em;",[569,1921],{},[569,1923],{"className":1924,"style":736},[735],[569,1926,698],{"className":1927},[740],[569,1929],{"className":1930,"style":736},[735],[569,1932,1934,1938],{"className":1933},[603],[569,1935],{"className":1936,"style":1937},[607],"height:0.6444em;",[569,1939,1669],{"className":1940},[612]," mit ",[569,1943,1945,1989],{"className":1944},[572],[569,1946,1948],{"className":1947},[576],[578,1949,1950],{"xmlns":580},[582,1951,1952,1986],{},[585,1953,1954,1967,1969,1971,1973,1976,1980,1982,1984],{},[1856,1955,1956,1965],{},[1957,1958,1959,1962],"mover",{"accent":599},[588,1960,1961],{},"v",[696,1963,1964],{},"⃗",[714,1966,716],{},[696,1968,698],{},[696,1970,1024],{"stretchy":1023},[714,1972,716],{},[696,1974,1975],{"separator":599},",",[1977,1978,1979],"mtext",{}," ",[696,1981,712],{},[714,1983,1669],{},[696,1985,1037],{"stretchy":1023},[592,1987,1988],{"encoding":594},"\\vec v_1 = (1,\\ 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= \\begin{pmatrix} 1 & 1 \\\\ -2 & 1 \\end{pmatrix}, \\quad D = \\begin{pmatrix} 2 & 0 \\\\ 0 & 5 \\end{pmatrix}, \\quad S^{-1} = \\frac{1}{3} \\begin{pmatrix} 1 & -1 \\\\ 2 & 1 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",[569,3108,3110,3140],{"className":3109},[572],[569,3111,3113],{"className":3112},[576],[578,3114,3115],{"xmlns":580},[582,3116,3117,3137],{},[585,3118,3119,3121,3123,3133,3135],{},[588,3120,633],{},[588,3122,664],{},[704,3124,3125,3127],{},[588,3126,633],{},[585,3128,3129,3131],{},[696,3130,712],{},[714,3132,716],{},[696,3134,698],{},[588,3136,590],{},[592,3138,3139],{"encoding":594},"S D S^{-1} = A",[569,3141,3143,3199],{"className":3142,"ariaHidden":599},[598],[569,3144,3146,3149,3152,3155,3190,3193,3196],{"className":3145},[603],[569,3147],{"className":3148,"style":750},[607],[569,3150,633],{"className":3151,"style":648},[612,613],[569,3153,664],{"className":3154,"style":679},[612,613],[569,3156,3158,3161],{"className":3157},[612],[569,3159,633],{"className":3160,"style":648},[612,613],[569,3162,3164],{"className":3163},[766],[569,3165,3167],{"className":3166},[770],[569,3168,3170],{"className":3169},[774],[569,3171,3173],{"className":3172,"style":750},[778],[569,3174,3175,3178],{"style":781},[569,3176],{"className":3177,"style":786},[785],[569,3179,3181],{"className":3180},[790,791,792,793],[569,3182,3184,3187],{"className":3183},[612,793],[569,3185,712],{"className":3186},[612,793],[569,3188,716],{"className":3189},[612,793],[569,3191],{"className":3192,"style":736},[735],[569,3194,698],{"className":3195},[740],[569,3197],{"className":3198,"style":736},[735],[569,3200,3202,3205],{"className":3201},[603],[569,3203],{"className":3204,"style":608},[607],[569,3206,590],{"className":3207},[612,613],". Für ",[569,3210,3212,3230],{"className":3211},[572],[569,3213,3215],{"className":3214},[576],[578,3216,3217],{"xmlns":580},[582,3218,3219,3227],{},[585,3220,3221],{},[704,3222,3223,3225],{},[588,3224,590],{},[714,3226,1676],{},[592,3228,3229],{"encoding":594},"A^3",[569,3231,3233],{"className":3232,"ariaHidden":599},[598],[569,3234,3236,3239],{"className":3235},[603],[569,3237],{"className":3238,"style":750},[607],[569,3240,3242,3245],{"className":3241},[612],[569,3243,590],{"className":3244},[612,613],[569,3246,3248],{"className":3247},[766],[569,3249,3251],{"className":3250},[770],[569,3252,3254],{"className":3253},[774],[569,3255,3257],{"className":3256,"style":750},[778],[569,3258,3259,3262],{"style":781},[569,3260],{"className":3261,"style":786},[785],[569,3263,3265],{"className":3264},[790,791,792,793],[569,3266,1676],{"className":3267},[612,793]," potenziert man nur die Diagonale:",[569,3270,3272],{"className":3271},[2384],[569,3273,3275,3478],{"className":3274},[572],[569,3276,3278],{"className":3277},[576],[578,3279,3280],{"xmlns":580,"display":2393},[582,3281,3282,3475],{},[585,3283,3284,3290,3292,3294,3332,3342,3344,3350,3391,3431,3433,3473],{},[704,3285,3286,3288],{},[588,3287,590],{},[714,3289,1676],{},[696,3291,698],{},[588,3293,633],{},[585,3295,3296,3298,3330],{},[696,3297,1024],{"fence":599},[1637,3299,3300,3315],{"rowspacing":1639,"columnalign":1640,"columnspacing":1641},[1643,3301,3302,3309],{},[1646,3303,3304],{},[1649,3305,3306],{"scriptlevel":1651,"displaystyle":1023},[714,3307,3308],{},"8",[1646,3310,3311],{},[1649,3312,3313],{"scriptlevel":1651,"displaystyle":1023},[714,3314,1651],{},[1643,3316,3317,3323],{},[1646,3318,3319],{},[1649,3320,3321],{"scriptlevel":1651,"displaystyle":1023},[714,3322,1651],{},[1646,3324,3325],{},[1649,3326,3327],{"scriptlevel":1651,"displaystyle":1023},[714,3328,3329],{},"125",[696,3331,1037],{"fence":599},[704,3333,3334,3336],{},[588,3335,633],{},[585,3337,3338,3340],{},[696,3339,712],{},[714,3341,716],{},[696,3343,698],{},[2503,3345,3346,3348],{},[714,3347,716],{},[714,3349,1676],{},[585,3351,3352,3354,3389],{},[696,3353,1024],{"fence":599},[1637,3355,3356,3370],{"rowspacing":1639,"columnalign":1640,"columnspacing":1641},[1643,3357,3358,3364],{},[1646,3359,3360],{},[1649,3361,3362],{"scriptlevel":1651,"displaystyle":1023},[714,3363,3308],{},[1646,3365,3366],{},[1649,3367,3368],{"scriptlevel":1651,"displaystyle":1023},[714,3369,3329],{},[1643,3371,3372,3383],{},[1646,3373,3374],{},[1649,3375,3376],{"scriptlevel":1651,"displaystyle":1023},[585,3377,3378,3380],{},[696,3379,712],{},[714,3381,3382],{},"16",[1646,3384,3385],{},[1649,3386,3387],{"scriptlevel":1651,"displaystyle":1023},[714,3388,3329],{},[696,3390,1037],{"fence":599},[585,3392,3393,3395,3429],{},[696,3394,1024],{"fence":599},[1637,3396,3397,3415],{"rowspacing":1639,"columnalign":1640,"columnspacing":1641},[1643,3398,3399,3405],{},[1646,3400,3401],{},[1649,3402,3403],{"scriptlevel":1651,"displaystyle":1023},[714,3404,716],{},[1646,3406,3407],{},[1649,3408,3409],{"scriptlevel":1651,"displaystyle":1023},[585,3410,3411,3413],{},[696,3412,712],{},[714,3414,716],{},[1643,3416,3417,3423],{},[1646,3418,3419],{},[1649,3420,3421],{"scriptlevel":1651,"displaystyle":1023},[714,3422,1669],{},[1646,3424,3425],{},[1649,3426,3427],{"scriptlevel":1651,"displaystyle":1023},[714,3428,716],{},[696,3430,1037],{"fence":599},[696,3432,698],{},[585,3434,3435,3437,3471],{},[696,3436,1024],{"fence":599},[1637,3438,3439,3455],{"rowspacing":1639,"columnalign":1640,"columnspacing":1641},[1643,3440,3441,3448],{},[1646,3442,3443],{},[1649,3444,3445],{"scriptlevel":1651,"displaystyle":1023},[714,3446,3447],{},"86",[1646,3449,3450],{},[1649,3451,3452],{"scriptlevel":1651,"displaystyle":1023},[714,3453,3454],{},"39",[1643,3456,3457,3464],{},[1646,3458,3459],{},[1649,3460,3461],{"scriptlevel":1651,"displaystyle":1023},[714,3462,3463],{},"78",[1646,3465,3466],{},[1649,3467,3468],{"scriptlevel":1651,"displaystyle":1023},[714,3469,3470],{},"47",[696,3472,1037],{"fence":599},[588,3474,1377],{"mathvariant":1107},[592,3476,3477],{"encoding":594},"A^3 = S \\begin{pmatrix} 8 & 0 \\\\ 0 & 125 \\end{pmatrix} S^{-1} = \\frac{1}{3} \\begin{pmatrix} 8 & 125 \\\\ -16 & 125 \\end{pmatrix} \\begin{pmatrix} 1 & -1 \\\\ 2 & 1 \\end{pmatrix} = \\begin{pmatrix} 86 & 39 \\\\ 78 & 47 \\end{pmatrix}.",[569,3479,3481,3525,3701,4024],{"className":3480,"ariaHidden":599},[598],[569,3482,3484,3487,3516,3519,3522],{"className":3483},[603],[569,3485],{"className":3486,"style":2877},[607],[569,3488,3490,3493],{"className":3489},[612],[569,3491,590],{"className":3492},[612,613],[569,3494,3496],{"className":3495},[766],[569,3497,3499],{"className":3498},[770],[569,3500,3502],{"className":3501},[774],[569,3503,3505],{"className":3504,"style":2877},[778],[569,3506,3507,3510],{"style":2880},[569,3508],{"className":3509,"style":786},[785],[569,3511,3513],{"className":3512},[790,791,792,793],[569,3514,1676],{"className":3515},[612,793],[569,3517],{"className":3518,"style":736},[735],[569,3520,698],{"className":3521},[740],[569,3523],{"className":3524,"style":736},[735],[569,3526,3528,3531,3534,3537,3654,3657,3692,3695,3698],{"className":3527},[603],[569,3529],{"className":3530,"style":1709},[607],[569,3532,633],{"className":3533,"style":648},[612,613],[569,3535],{"className":3536,"style":2120},[735],[569,3538,3540,3546,3648],{"className":3539},[1713],[569,3541,3543],{"className":3542,"style":1718},[1058,1717],[569,3544,1024],{"className":3545},[1722,792],[569,3547,3549],{"className":3548},[612],[569,3550,3552,3597,3600,3603],{"className":3551},[1637],[569,3553,3555],{"className":3554},[1732],[569,3556,3558,3589],{"className":3557},[770,1736],[569,3559,3561,3586],{"className":3560},[774],[569,3562,3564,3575],{"className":3563,"style":1743},[778],[569,3565,3566,3569],{"style":1746},[569,3567],{"className":3568,"style":1750},[785],[569,3570,3572],{"className":3571},[612],[569,3573,3308],{"className":3574},[612],[569,3576,3577,3580],{"style":1759},[569,3578],{"className":3579,"style":1750},[785],[569,3581,3583],{"className":3582},[612],[569,3584,1651],{"className":3585},[612],[569,3587,1773],{"className":3588},[1772],[569,3590,3592],{"className":3591},[774],[569,3593,3595],{"className":3594,"style":1780},[778],[569,3596],{},[569,3598],{"className":3599,"style":1787},[1786],[569,3601],{"className":3602,"style":1787},[1786],[569,3604,3606],{"className":3605},[1732],[569,3607,3609,3640],{"className":3608},[770,1736],[569,3610,3612,3637],{"className":3611},[774],[569,3613,3615,3626],{"className":3614,"style":1743},[778],[569,3616,3617,3620],{"style":1746},[569,3618],{"className":3619,"style":1750},[785],[569,3621,3623],{"className":3622},[612],[569,3624,1651],{"className":3625},[612],[569,3627,3628,3631],{"style":1759},[569,3629],{"className":3630,"style":1750},[785],[569,3632,3634],{"className":3633},[612],[569,3635,3329],{"className":3636},[612],[569,3638,1773],{"className":3639},[1772],[569,3641,3643],{"className":3642},[774],[569,3644,3646],{"className":3645,"style":1780},[778],[569,3647],{},[569,3649,3651],{"className":3650,"style":1718},[1088,1717],[569,3652,1037],{"className":3653},[1722,792],[569,3655],{"className":3656,"style":2120},[735],[569,3658,3660,3663],{"className":3659},[612],[569,3661,633],{"className":3662,"style":648},[612,613],[569,3664,3666],{"className":3665},[766],[569,3667,3669],{"className":3668},[770],[569,3670,3672],{"className":3671},[774],[569,3673,3675],{"className":3674,"style":2877},[778],[569,3676,3677,3680],{"style":2880},[569,3678],{"className":3679,"style":786},[785],[569,3681,3683],{"className":3682},[790,791,792,793],[569,3684,3686,3689],{"className":3685},[612,793],[569,3687,712],{"className":3688},[612,793],[569,3690,716],{"className":3691},[612,793],[569,3693],{"className":3694,"style":736},[735],[569,3696,698],{"className":3697},[740],[569,3699],{"className":3700,"style":736},[735],[569,3702,3704,3707,3769,3772,3892,3895,4015,4018,4021],{"className":3703},[603],[569,3705],{"className":3706,"style":1709},[607],[569,3708,3710,3713,3766],{"className":3709},[612],[569,3711],{"className":3712},[1058,2917],[569,3714,3716],{"className":3715},[2503],[569,3717,3719,3758],{"className":3718},[770,1736],[569,3720,3722,3755],{"className":3721},[774],[569,3723,3725,3736,3744],{"className":3724,"style":2930},[778],[569,3726,3727,3730],{"style":2933},[569,3728],{"className":3729,"style":1750},[785],[569,3731,3733],{"className":3732},[612],[569,3734,1676],{"className":3735},[612],[569,3737,3738,3741],{"style":2945},[569,3739],{"className":3740,"style":1750},[785],[569,3742],{"className":3743,"style":2953},[2952],[569,3745,3746,3749],{"style":2956},[569,3747],{"className":3748,"style":1750},[785],[569,3750,3752],{"className":3751},[612],[569,3753,716],{"className":3754},[612],[569,3756,1773],{"className":3757},[1772],[569,3759,3761],{"className":3760},[774],[569,3762,3764],{"className":3763,"style":2975},[778],[569,3765],{},[569,3767],{"className":3768},[1088,2917],[569,3770],{"className":3771,"style":2120},[735],[569,3773,3775,3781,3886],{"className":3774},[1713],[569,3776,3778],{"className":3777,"style":1718},[1058,1717],[569,3779,1024],{"className":3780},[1722,792],[569,3782,3784],{"className":3783},[612],[569,3785,3787,3835,3838,3841],{"className":3786},[1637],[569,3788,3790],{"cla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\\end{pmatrix}",[569,4206,4208],{"className":4207,"ariaHidden":599},[598],[569,4209,4211,4214],{"className":4210},[603],[569,4212],{"className":4213,"style":1709},[607],[569,4215,4217,4223,4325],{"className":4216},[1713],[569,4218,4220],{"className":4219,"style":1718},[1058,1717],[569,4221,1024],{"className":4222},[1722,792],[569,4224,4226],{"className":4225},[612],[569,4227,4229,4274,4277,4280],{"className":4228},[1637],[569,4230,4232],{"className":4231},[1732],[569,4233,4235,4266],{"className":4234},[770,1736],[569,4236,4238,4263],{"className":4237},[774],[569,4239,4241,4252],{"className":4240,"style":1743},[778],[569,4242,4243,4246],{"style":1746},[569,4244],{"className":4245,"style":1750},[785],[569,4247,4249],{"className":4248},[612],[569,4250,716],{"className":4251},[612],[569,4253,4254,4257],{"style":1759},[569,4255],{"className":4256,"style":1750},[785],[569,4258,4260],{"className":4259},[612],[569,4261,1651],{"className":4262},[612],[569,4264,1773],{"className":4265},[1772],[569,4267,4269],{"className":4268},[774],[569,4270,4272],{"className":4271,"style":1780},[778],[569,4273],{},[569,4275],{"className":4276,"style":1787},[1786],[569,4278],{"className":4279,"style":1787},[1786],[569,4281,4283],{"className":4282},[1732],[569,4284,4286,4317],{"className":4285},[770,1736],[569,4287,4289,4314],{"className":4288},[774],[569,4290,4292,4303],{"className":4291,"style":1743},[778],[569,4293,4294,4297],{"style":1746},[569,4295],{"className":4296,"style":1750},[785],[569,4298,4300],{"className":4299},[612],[569,4301,716],{"className":4302},[612],[569,4304,4305,4308],{"style":1759},[569,4306],{"className":4307,"style":1750},[785],[569,4309,4311],{"className":4310},[612],[569,4312,716],{"className":4313},[612],[569,4315,1773],{"className":4316},[1772],[569,4318,4320],{"className":4319},[774],[569,4321,4323],{"className":4322,"style":1780},[778],[569,4324],{},[569,4326,4328],{"className":4327,"style":1718},[1088,1717],[569,4329,1037],{"className":4330},[1722,792]," hat das charakteristische Polynom ",[569,4333,4335,4361],{"className":4334},[572],[569,4336,4338],{"className":4337},[576],[578,4339,4340],{"xmlns":580},[582,4341,4342,4358],{},[585,4343,4344,4346,4348,4350,4352],{},[696,4345,1024],{"stretchy":1023},[714,4347,716],{},[696,4349,712],{},[588,4351,1031],{},[704,4353,4354,4356],{},[696,4355,1037],{"stretchy":1023},[714,4357,1669],{},[592,4359,4360],{"encoding":594},"(1 - \\lambda)^2",[569,4362,4364,4385],{"className":4363,"ariaHidden":599},[598],[569,4365,4367,4370,4373,4376,4379,4382],{"className":4366},[603],[569,4368],{"className":4369,"style":1050},[607],[569,4371,1024],{"className":4372},[1058],[569,4374,716],{"className":4375},[612],[569,4377],{"className":4378,"style":1065},[735],[569,4380,712],{"className":4381},[1069],[569,4383],{"className":4384,"style":1065},[735],[569,4386,4388,4392,4395],{"className":4387},[603],[569,4389],{"className":4390,"style":4391},[607],"height:1.0641em;vertical-align:-0.25em;",[569,4393,1031],{"className":4394},[612,613],[569,4396,4398,4401],{"className":4397},[1088],[569,4399,1037],{"className":4400},[1088],[569,4402,4404],{"className":4403},[766],[569,4405,4407],{"className":4406},[770],[569,4408,4410],{"className":4409},[774],[569,4411,4413],{"className":4412,"style":750},[778],[569,4414,4415,4418],{"style":781},[569,4416],{"className":4417,"style":786},[785],[569,4419,4421],{"className":4420},[790,791,792,793],[569,4422,1669],{"className":4423},[612,793],", also den doppelten Eigenwert ",[569,4426,4428,4441],{"className":4427},[572],[569,4429,4431],{"className":4430},[576],[578,4432,4433],{"xmlns":580},[582,4434,4435,4439],{},[585,4436,4437],{},[714,4438,716],{},[592,4440,716],{"encoding":594},[569,4442,4444],{"className":4443,"ariaHidden":599},[598],[569,4445,4447,4450],{"className":4446},[603],[569,4448],{"className":4449,"style":1937},[607],[569,4451,716],{"className":4452},[612],". Der Eigenraum ",[569,4455,4457,4509],{"className":4456},[572],[569,4458,4460],{"className":4459},[576],[578,4461,4462],{"xmlns":580},[582,4463,4464,4506],{},[585,4465,4466,4468,4470],{},[588,4467,1108],{"mathvariant":1107},[696,4469,1020],{},[585,4471,4472,4474,4504],{},[696,4473,1024],{"fence":599},[1637,4475,4476,4490],{"rowspacing":1639,"columnalign":1640,"columnspacing":1641},[1643,4477,4478,4484],{},[1646,4479,4480],{},[1649,4481,4482],{"scriptlevel":1651,"displaystyle":1023},[714,4483,1651],{},[1646,4485,4486],{},[1649,4487,4488],{"scriptlevel":1651,"displaystyle":1023},[714,4489,716],{},[1643,4491,4492,4498],{},[1646,4493,4494],{},[1649,4495,4496],{"scriptlevel":1651,"displaystyle":1023},[714,4497,1651],{},[1646,4499,4500],{},[1649,4501,4502],{"scriptlevel":1651,"displaystyle":1023},[714,4503,1651],{},[696,4505,1037],{"fence":599},[592,4507,4508],{"encoding":594},"\\operatorname{Kern}\\begin{pmatrix} 0 & 1 \\\\ 0 & 0 \\end{pmatrix}",[569,4510,4512],{"className":4511,"ariaHidden":599},[598],[569,4513,4515,4518,4524,4527],{"className":4514},[603],[569,4516],{"className":4517,"style":1709},[607],[569,4519,4521],{"className":4520},[1054],[569,4522,1108],{"className":4523},[612,1141],[569,4525],{"className":4526,"style":2120},[735],[569,4528,4530,4536,4638],{"className":4529},[1713],[569,4531,4533],{"className":4532,"style":1718},[1058,1717],[569,4534,1024],{"className":4535},[1722,792],[569,4537,4539],{"className":4538},[612],[569,4540,4542,4587,4590,4593],{"className":4541},[1637],[569,4543,4545],{"className":4544},[1732],[569,4546,4548,4579],{"className":4547},[770,1736],[569,4549,4551,4576],{"className":4550},[774],[569,4552,4554,4565],{"className":4553,"style":1743},[778],[569,4555,4556,4559],{"style":1746},[569,4557],{"className":4558,"style":1750},[785],[569,4560,4562],{"className":4561},[612],[569,4563,1651],{"className":4564},[612],[569,4566,4567,4570],{"style":1759},[569,4568],{"className":4569,"style":1750},[785],[569,4571,4573],{"className":4572},[612],[569,4574,1651],{"className":4575},[612],[569,4577,1773],{"className":4578},[1772],[569,4580,4582],{"className":4581},[774],[569,4583,4585],{"className":4584,"style":1780},[778],[569,4586],{},[569,4588],{"className":4589,"style":1787},[1786],[569,4591],{"className":4592,"style":1787},[1786],[569,4594,4596],{"className":4595},[1732],[569,4597,4599,4630],{"className":4598},[770,1736],[569,4600,4602,4627],{"className":4601},[774],[569,4603,4605,4616],{"className":4604,"style":1743},[778],[569,4606,4607,4610],{"style":1746},[569,4608],{"className":4609,"style":1750},[785],[569,4611,4613],{"className":4612},[612],[569,4614,716],{"className":4615},[612],[569,4617,4618,4621],{"style":1759},[569,4619],{"className":4620,"style":1750},[785],[569,4622,4624],{"className":4623},[612],[569,4625,1651],{"className":4626},[612],[569,4628,1773],{"className":4629},[1772],[569,4631,4633],{"className":4632},[774],[569,4634,4636],{"className":4635,"style":1780},[778],[569,4637],{},[569,4639,4641],{"className":4640,"style":1718},[1088,1717],[569,4642,1037],{"className":4643},[1722,792]," ist aber nur eindimensional. Es gibt keine zwei unabhängigen Eigenvektoren, die Matrix ist nicht diagonalisierbar.",[560,4646,4648],{"id":4647},"typische-fehler","Typische Fehler",[1269,4650,4651,4683,4744,5140],{},[1000,4652,4653,4654,4682],{},"Eigenvektoren als Zeilen statt als Spalten in ",[569,4655,4657,4670],{"className":4656},[572],[569,4658,4660],{"className":4659},[576],[578,4661,4662],{"xmlns":580},[582,4663,4664,4668],{},[585,4665,4666],{},[588,4667,633],{},[592,4669,633],{"encoding":594},[569,4671,4673],{"className":4672,"ariaHidden":599},[598],[569,4674,4676,4679],{"className":4675},[603],[569,4677],{"className":4678,"style":608},[607],[569,4680,633],{"className":4681,"style":648},[612,613]," schreiben.",[1000,4684,4685,4686,4714,4715,4743],{},"Die Reihenfolge in ",[569,4687,4689,4702],{"className":4688},[572],[569,4690,4692],{"className":4691},[576],[578,4693,4694],{"xmlns":580},[582,4695,4696,4700],{},[585,4697,4698],{},[588,4699,664],{},[592,4701,664],{"encoding":594},[569,4703,4705],{"className":4704,"ariaHidden":599},[598],[569,4706,4708,4711],{"className":4707},[603],[569,4709],{"className":4710,"style":608},[607],[569,4712,664],{"className":4713,"style":679},[612,613]," nicht an die Reihenfolge der Spalten von ",[569,4716,4718,4731],{"className":4717},[572],[569,4719,4721],{"className":4720},[576],[578,4722,4723],{"xmlns":580},[582,4724,4725,4729],{},[585,4726,4727],{},[588,4728,633],{},[592,4730,633],{"encoding":594},[569,4732,4734],{"className":4733,"ariaHidden":599},[598],[569,4735,4737,4740],{"className":4736},[603],[569,4738],{"className":4739,"style":608},[607],[569,4741,633],{"className":4742,"style":648},[612,613]," anpassen.",[1000,4745,4746,4847,4848,4948,4949,4977,4978,5039,5040,1377],{},[569,4747,4749,4779],{"className":4748},[572],[569,4750,4752],{"className":4751},[576],[578,4753,4754],{"xmlns":580},[582,4755,4756,4776],{},[585,4757,4758,4760,4762,4772,4774],{},[588,4759,590],{},[696,4761,698],{},[704,4763,4764,4766],{},[588,4765,633],{},[585,4767,4768,4770],{},[696,4769,712],{},[714,4771,716],{},[588,4773,664],{},[588,4775,633],{},[592,4777,4778],{"encoding":594},"A = S^{-1} D S",[569,4780,4782,4800],{"className":4781,"ariaHidden":599},[598],[569,4783,4785,4788,4791,4794,4797],{"className":4784},[603],[569,4786],{"className":4787,"style":608},[607],[569,4789,590],{"className":4790},[612,613],[569,4792],{"className":4793,"style":736},[735],[569,4795,698],{"className":4796},[740],[569,4798],{"className":4799,"style":736},[735],[569,4801,4803,4806,4841,4844],{"className":4802},[603],[569,4804],{"className":4805,"style":750},[607],[569,4807,4809,4812],{"className":4808},[612],[569,4810,633],{"className":4811,"style":648},[612,613],[569,4813,4815],{"className":4814},[766],[569,4816,4818],{"className":4817},[770],[569,4819,4821],{"className":4820},[774],[569,4822,4824],{"className":4823,"style":750},[778],[569,4825,4826,4829],{"style":781},[569,4827],{"className":4828,"style":786},[785],[569,4830,4832],{"className":4831},[790,791,792,793],[569,4833,4835,4838],{"className":4834},[612,793],[569,4836,712],{"className":4837},[612,793],[569,4839,716],{"className":4840},[612,793],[569,4842,664],{"className":4843,"style":679},[612,613],[569,4845,633],{"className":4846,"style":648},[612,613]," statt ",[569,4849,4851,4880],{"className":4850},[572],[569,4852,4854],{"className":4853},[576],[578,4855,4856],{"xmlns":580},[582,4857,4858,4878],{},[585,4859,4860,4862,4864,4866,4868],{},[588,4861,590],{},[696,4863,698],{},[588,4865,633],{},[588,4867,664],{},[704,4869,4870,4872],{},[588,4871,633],{},[585,4873,4874,4876],{},[696,4875,712],{},[714,4877,716],{},[592,4879,719],{"encoding":594},[569,4881,4883,4901],{"className":4882,"ariaHidden":599},[598],[569,4884,4886,4889,4892,4895,4898],{"className":4885},[603],[569,4887],{"className":4888,"style":608},[607],[569,4890,590],{"className":4891},[612,613],[569,4893],{"className":4894,"style":736},[735],[569,4896,698],{"className":4897},[740],[569,4899],{"className":4900,"style":736},[735],[569,4902,4904,4907,4910,4913],{"className":4903},[603],[569,4905],{"className":4906,"style":750},[607],[569,4908,633],{"className":4909,"style":648},[612,613],[569,4911,664],{"className":4912,"style":679},[612,613],[569,4914,4916,4919],{"className":4915},[612],[569,4917,633],{"className":4918,"style":648},[612,613],[569,4920,4922],{"className":4921},[766],[569,4923,4925],{"className":4924},[770],[569,4926,4928],{"className":4927},[774],[569,4929,4931],{"className":4930,"style":750},[778],[569,4932,4933,4936],{"style":781},[569,4934],{"className":4935,"style":786},[785],[569,4937,4939],{"className":4938},[790,791,792,793],[569,4940,4942,4945],{"className":4941},[612,793],[569,4943,712],{"className":4944},[612,793],[569,4946,716],{"className":4947},[612,793]," schreiben. Mit Eigenvektoren als Spalten von ",[569,4950,4952,4965],{"className":4951},[572],[569,4953,4955],{"className":4954},[576],[578,4956,4957],{"xmlns":580},[582,4958,4959,4963],{},[585,4960,4961],{},[588,4962,633],{},[592,4964,633],{"encoding":594},[569,4966,4968],{"className":4967,"ariaHidden":599},[598],[569,4969,4971,4974],{"className":4970},[603],[569,4972],{"className":4973,"style":608},[607],[569,4975,633],{"className":4976,"style":648},[612,613]," gilt ",[569,4979,4981,5003],{"className":4980},[572],[569,4982,4984],{"className":4983},[576],[578,4985,4986],{"xmlns":580},[582,4987,4988,5000],{},[585,4989,4990,4992,4994,4996,4998],{},[588,4991,590],{},[588,4993,633],{},[696,4995,698],{},[588,4997,633],{},[588,4999,664],{},[592,5001,5002],{"encoding":594},"AS = SD",[569,5004,5006,5027],{"className":5005,"ariaHidden":599},[598],[569,5007,5009,5012,5015,5018,5021,5024],{"className":5008},[603],[569,5010],{"className":5011,"style":608},[607],[569,5013,590],{"className":5014},[612,613],[569,5016,633],{"className":5017,"style":648},[612,613],[569,5019],{"className":5020,"style":736},[735],[569,5022,698],{"className":5023},[740],[569,5025],{"className":5026,"style":736},[735],[569,5028,5030,5033,5036],{"className":5029},[603],[569,5031],{"className":5032,"style":608},[607],[569,5034,633],{"className":5035,"style":648},[612,613],[569,5037,664],{"className":5038,"style":679},[612,613],", also ",[569,5041,5043,5072],{"className":5042},[572],[569,5044,5046],{"className":5045},[576],[578,5047,5048],{"xmlns":580},[582,5049,5050,5070],{},[585,5051,5052,5054,5056,5058,5060],{},[588,5053,590],{},[696,5055,698],{},[588,5057,633],{},[588,5059,664],{},[704,5061,5062,5064],{},[588,5063,633],{},[585,5065,5066,5068],{},[696,5067,712],{},[714,5069,716],{},[592,5071,719],{"encoding":594},[569,5073,5075,5093],{"className":5074,"ariaHidden":599},[598],[569,5076,5078,5081,5084,5087,5090],{"className":5077},[603],[569,5079],{"className":5080,"style":608},[607],[569,5082,590],{"className":5083},[612,613],[569,5085],{"className":5086,"style":736},[735],[569,5088,698],{"className":5089},[740],[569,5091],{"className":5092,"style":736},[735],[569,5094,5096,5099,5102,5105],{"className":5095},[603],[569,5097],{"className":5098,"style":750},[607],[569,5100,633],{"className":5101,"style":648},[612,613],[569,5103,664],{"className":5104,"style":679},[612,613],[569,5106,5108,5111],{"className":5107},[612],[569,5109,633],{"className":5110,"style":648},[612,613],[569,5112,5114],{"className":5113},[766],[569,5115,5117],{"className":5116},[770],[569,5118,5120],{"className":5119},[774],[569,5121,5123],{"className":5122,"style":750},[778],[569,5124,5125,5128],{"style":781},[569,5126],{"className":5127,"style":786},[785],[569,5129,5131],{"className":5130},[790,791,792,793],[569,5132,5134,5137],{"className":5133},[612,793],[569,5135,712],{"className":5136},[612,793],[569,5138,716],{"className":5139},[612,793],[1000,5141,5142,5143,5171,5172,5200],{},"Aus einem doppelten Eigenwert schließen, dass ",[569,5144,5146,5159],{"className":5145},[572],[569,5147,5149],{"className":5148},[576],[578,5150,5151],{"xmlns":580},[582,5152,5153,5157],{},[585,5154,5155],{},[588,5156,590],{},[592,5158,590],{"encoding":594},[569,5160,5162],{"className":5161,"ariaHidden":599},[598],[569,5163,5165,5168],{"className":5164},[603],[569,5166],{"className":5167,"style":608},[607],[569,5169,590],{"className":5170},[612,613]," nicht diagonalisierbar ist. Die Einheitsmatrix hat nur den Eigenwert ",[569,5173,5175,5188],{"className":5174},[572],[569,5176,5178],{"className":5177},[576],[578,5179,5180],{"xmlns":580},[582,5181,5182,5186],{},[585,5183,5184],{},[714,5185,716],{},[592,5187,716],{"encoding":594},[569,5189,5191],{"className":5190,"ariaHidden":599},[598],[569,5192,5194,5197],{"className":5193},[603],[569,5195],{"className":5196,"style":1937},[607],[569,5198,716],{"className":5199},[612]," und ist schon diagonal. Entscheidend ist die Dimension des Eigenraums.",{"title":5202,"searchDepth":5203,"depth":5203,"links":5204},"",2,[5205,5206,5207],{"id":562,"depth":5203,"text":563},{"id":1612,"depth":5203,"text":1613},{"id":4647,"depth":5203,"text":4648},[5209,5211,5214,5217,5219,5221,5223,5225,5227,5229,5231,5233,5235,5237,5239,5241],{"lhs":5210,"rhs":1676},"det([[1, 1], [-2, 1]])",{"lhs":5212,"rhs":5213},"inv([[1, 1], [-2, 1]])[1, 2]","-1\u002F3",{"lhs":5215,"rhs":5216},"inv([[1, 1], [-2, 1]])[2, 1]","2\u002F3",{"lhs":5218,"rhs":1654},"multiply(multiply([[1, 1], [-2, 1]], [[2, 0], [0, 5]]), inv([[1, 1], [-2, 1]]))[1, 1]",{"lhs":5220,"rhs":716},"multiply(multiply([[1, 1], [-2, 1]], [[2, 0], [0, 5]]), inv([[1, 1], [-2, 1]]))[1, 2]",{"lhs":5222,"rhs":1669},"multiply(multiply([[1, 1], [-2, 1]], [[2, 0], [0, 5]]), inv([[1, 1], [-2, 1]]))[2, 1]",{"lhs":5224,"rhs":1676},"multiply(multiply([[1, 1], [-2, 1]], [[2, 0], [0, 5]]), inv([[1, 1], [-2, 1]]))[2, 2]",{"lhs":5226,"rhs":3308},"2^3",{"lhs":5228,"rhs":3329},"5^3",{"lhs":5230,"rhs":3447},"(8*1 + 125*2)\u002F3",{"lhs":5232,"rhs":3454},"(8*(-1) + 125*1)\u002F3",{"lhs":5234,"rhs":3463},"(-16*1 + 125*2)\u002F3",{"lhs":5236,"rhs":3470},"(-16*(-1) + 125*1)\u002F3",{"lhs":5238,"rhs":3454},"multiply([[4, 1], [2, 3]], multiply([[4, 1], [2, 3]], [[4, 1], [2, 3]]))[1, 2]",{"lhs":5240,"rhs":3463},"multiply([[4, 1], [2, 3]], multiply([[4, 1], [2, 3]], [[4, 1], [2, 3]]))[2, 1]",{"lhs":5242,"rhs":5243},"det([[1 - x, 1], [0, 1 - x]])","(1 - x)^2","A \\in \\mathbb{R}^{n \\times n} \\text{ hat } n \\text{ linear unabhängige Eigenvektoren } \\vec v_1, \\ldots, \\vec v_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> \u003Cspan class=\"katex\">hat\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">linear unabhängige Eigenvektoren\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec v_1, \\ldots, \\vec v_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">v\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","diagonalization","A = S D S^{-1}, \\qquad D = \\begin{pmatrix} \\lambda_1 & & \\\\ & \\ddots & \\\\ & & \\lambda_n \\end{pmatrix}, \\qquad S = (\\vec v_1 \\mid \\cdots \\mid \\vec v_n)","\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>A\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>S\u003C\u002Fmi>\u003Cmi>D\u003C\u002Fmi>\u003Cmsup>\u003Cmi>S\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>D\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmtable rowspacing=\"0.16em\" columnalign=\"center center center\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmo lspace=\"0em\" rspace=\"0em\">⋱\u003C\u002Fmo>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmsub>\u003Cmi>λ\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>S\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>∣\u003C\u002Fmo>\u003Cmo>⋯\u003C\u002Fmo>\u003Cmo>∣\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A = S D S^{-1}, \\qquad D = \\begin{pmatrix} \\lambda_1 & & \\\\ & \\ddots & \\\\ & & \\lambda_n \\end{pmatrix}, \\qquad S = (\\vec v_1 \\mid \\cdots \\mid \\vec v_n)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\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:1.0585em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">D\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan 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