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Deshalb ist jede Spaltensumme ",[587,698,700,715],{"className":699},[590],[587,701,703],{"className":702},[594],[596,704,705],{"xmlns":598},[600,706,707,713],{},[603,708,709],{},[710,711,712],"mn",{},"1",[610,714,712],{"encoding":612},[587,716,718],{"className":717,"ariaHidden":617},[616],[587,719,721,725],{"className":720},[621],[587,722],{"className":723,"style":724},[625],"height:0.6444em;",[587,726,712],{"className":727},[630]," (",[569,730,731],{},"stochastische Matrix","). Der Zustandsvektor ",[587,734,736,764],{"className":735},[590],[587,737,739],{"className":738},[594],[596,740,741],{"xmlns":598},[600,742,743,761],{},[603,744,745],{},[746,747,748,758],"msub",{},[749,750,751,754],"mover",{"accent":617},[606,752,753],{},"v",[755,756,757],"mo",{},"⃗",[606,759,760],{},"n",[610,762,763],{"encoding":612},"\\vec{v}_n",[587,765,767],{"className":766,"ariaHidden":617},[616],[587,768,770,774],{"className":769},[621],[587,771],{"className":772,"style":773},[625],"height:0.864em;vertical-align:-0.15em;",[587,775,777,834],{"className":776},[630],[587,778,781],{"className":779},[630,780],"accent",[587,782,785],{"className":783},[784],"vlist-t",[587,786,789],{"className":787},[788],"vlist-r",[587,790,794,806],{"className":791,"style":793},[792],"vlist","height:0.714em;",[587,795,797,802],{"style":796},"top:-3em;",[587,798],{"className":799,"style":801},[800],"pstrut","height:3em;",[587,803,753],{"className":804,"style":805},[630,631],"margin-right:0.0359em;",[587,807,808,811],{"style":796},[587,809],{"className":810,"style":801},[800],[587,812,816],{"className":813,"style":815},[814],"accent-body","left:-0.2077em;",[587,817,821],{"className":818,"style":820},[819],"overlay","height:0.714em;width:0.471em;",[822,823,830],"svg",{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[831,832],"path",{"d":833},"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",[587,835,838],{"className":836},[837],"msupsub",[587,839,842,871],{"className":840},[784,841],"vlist-t2",[587,843,845,866],{"className":844},[788],[587,846,849],{"className":847,"style":848},[792],"height:0.1514em;",[587,850,852,856],{"style":851},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[587,853],{"className":854,"style":855},[800],"height:2.7em;",[587,857,863],{"className":858},[859,860,861,862],"sizing","reset-size6","size3","mtight",[587,864,760],{"className":865},[630,631,862],[587,867,870],{"className":868},[869],"vlist-s","​",[587,872,874],{"className":873},[788],[587,875,878],{"className":876,"style":877},[792],"height:0.15em;",[587,879],{}," enthält die Wahrscheinlichkeiten der Zustände nach ",[587,882,884,897],{"className":883},[590],[587,885,887],{"className":886},[594],[596,888,889],{"xmlns":598},[600,890,891,895],{},[603,892,893],{},[606,894,760],{},[610,896,760],{"encoding":612},[587,898,900],{"className":899,"ariaHidden":617},[616],[587,901,903,907],{"className":902},[621],[587,904],{"className":905,"style":906},[625],"height:0.4306em;",[587,908,760],{"className":909},[630,631]," Schritten. Ein Schritt ist eine Matrix-Vektor-Multiplikation, ",[587,912,914,927],{"className":913},[590],[587,915,917],{"className":916},[594],[596,918,919],{"xmlns":598},[600,920,921,925],{},[603,922,923],{},[606,924,760],{},[610,926,760],{"encoding":612},[587,928,930],{"className":929,"ariaHidden":617},[616],[587,931,933,936],{"className":932},[621],[587,934],{"className":935,"style":906},[625],[587,937,760],{"className":938},[630,631]," Schritte entsprechen der Matrixpotenz ",[587,941,943,962],{"className":942},[590],[587,944,946],{"className":945},[594],[596,947,948],{"xmlns":598},[600,949,950,959],{},[603,951,952],{},[953,954,955,957],"msup",{},[606,956,608],{},[606,958,760],{},[610,960,961],{"encoding":612},"A^n",[587,963,965],{"className":964,"ariaHidden":617},[616],[587,966,968,971],{"className":967},[621],[587,969],{"className":970,"style":626},[625],[587,972,974,977],{"className":973},[630],[587,975,608],{"className":976},[630,631],[587,978,980],{"className":979},[837],[587,981,983],{"className":982},[784],[587,984,986],{"className":985},[788],[587,987,990],{"className":988,"style":989},[792],"height:0.6644em;",[587,991,993,996],{"style":992},"top:-3.063em;margin-right:0.05em;",[587,994],{"className":995,"style":855},[800],[587,997,999],{"className":998},[859,860,861,862],[587,1000,760],{"className":1001},[630,631,862],".",[565,1004,1005,1006,1134,1135,1163,1164,1192,1193,1222],{},"Der Eintrag ",[587,1007,1009,1043],{"className":1008},[590],[587,1010,1012],{"className":1011},[594],[596,1013,1014],{"xmlns":598},[600,1015,1016,1040],{},[603,1017,1018,1022,1028],{},[755,1019,1021],{"stretchy":1020},"false","(",[953,1023,1024,1026],{},[606,1025,608],{},[606,1027,760],{},[746,1029,1030,1033],{},[755,1031,1032],{"stretchy":1020},")",[603,1034,1035,1038],{},[606,1036,1037],{},"i",[606,1039,650],{},[610,1041,1042],{"encoding":612},"(A^n)_{ij}",[587,1044,1046],{"className":1045,"ariaHidden":617},[616],[587,1047,1049,1053,1057,1086],{"className":1048},[621],[587,1050],{"className":1051,"style":1052},[625],"height:1.0361em;vertical-align:-0.2861em;",[587,1054,1021],{"className":1055},[1056],"mopen",[587,1058,1060,1063],{"className":1059},[630],[587,1061,608],{"className":1062},[630,631],[587,1064,1066],{"className":1065},[837],[587,1067,1069],{"className":1068},[784],[587,1070,1072],{"className":1071},[788],[587,1073,1075],{"className":1074,"style":989},[792],[587,1076,1077,1080],{"style":992},[587,1078],{"className":1079,"style":855},[800],[587,1081,1083],{"className":1082},[859,860,861,862],[587,1084,760],{"className":1085},[630,631,862],[587,1087,1090,1093],{"className":1088},[1089],"mclose",[587,1091,1032],{"className":1092},[1089],[587,1094,1096],{"className":1095},[837],[587,1097,1099,1125],{"className":1098},[784,841],[587,1100,1102,1122],{"className":1101},[788],[587,1103,1106],{"className":1104,"style":1105},[792],"height:0.3117em;",[587,1107,1109,1112],{"style":1108},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[587,1110],{"className":1111,"style":855},[800],[587,1113,1115],{"className":1114},[859,860,861,862],[587,1116,1118],{"className":1117},[630,862],[587,1119,1121],{"className":1120,"style":666},[630,631,862],"ij",[587,1123,870],{"className":1124},[869],[587,1126,1128],{"className":1127},[788],[587,1129,1132],{"className":1130,"style":1131},[792],"height:0.2861em;",[587,1133],{}," ist die Wahrscheinlichkeit, in ",[587,1136,1138,1151],{"className":1137},[590],[587,1139,1141],{"className":1140},[594],[596,1142,1143],{"xmlns":598},[600,1144,1145,1149],{},[603,1146,1147],{},[606,1148,760],{},[610,1150,760],{"encoding":612},[587,1152,1154],{"className":1153,"ariaHidden":617},[616],[587,1155,1157,1160],{"className":1156},[621],[587,1158],{"className":1159,"style":906},[625],[587,1161,760],{"className":1162},[630,631]," Schritten von ",[587,1165,1167,1180],{"className":1166},[590],[587,1168,1170],{"className":1169},[594],[596,1171,1172],{"xmlns":598},[600,1173,1174,1178],{},[603,1175,1176],{},[606,1177,650],{},[610,1179,650],{"encoding":612},[587,1181,1183],{"className":1182,"ariaHidden":617},[616],[587,1184,1186,1189],{"className":1185},[621],[587,1187],{"className":1188,"style":662},[625],[587,1190,650],{"className":1191,"style":666},[630,631]," nach ",[587,1194,1196,1209],{"className":1195},[590],[587,1197,1199],{"className":1198},[594],[596,1200,1201],{"xmlns":598},[600,1202,1203,1207],{},[603,1204,1205],{},[606,1206,1037],{},[610,1208,1037],{"encoding":612},[587,1210,1212],{"className":1211,"ariaHidden":617},[616],[587,1213,1215,1219],{"className":1214},[621],[587,1216],{"className":1217,"style":1218},[625],"height:0.6595em;",[587,1220,1037],{"className":1221},[630,631]," zu gelangen. Die Wahrscheinlichkeit eines bestimmten Pfades ist das Produkt der Übergangswahrscheinlichkeiten entlang des Pfades.",[565,1224,1225,1226,1229,1230,1521,1522,1603,1604,1002],{},"Hinweis: Viele Hochschulbücher schreiben die Wahrscheinlichkeiten in ",[569,1227,1228],{},"Zeilen"," und rechnen mit Zeilenvektoren, ",[587,1231,1233,1294],{"className":1232},[590],[587,1234,1236],{"className":1235},[594],[596,1237,1238],{"xmlns":598},[600,1239,1240,1291],{},[603,1241,1242,1269,1272,1288],{},[1243,1244,1245,1251,1260],"msubsup",{},[749,1246,1247,1249],{"accent":617},[606,1248,753],{},[755,1250,757],{},[603,1252,1253,1255,1258],{},[606,1254,760],{},[755,1256,1257],{},"+",[710,1259,712],{},[603,1261,1262,1266],{},[1263,1264,1265],"mtext",{}," ",[606,1267,1268],{},"T",[755,1270,1271],{},"=",[1243,1273,1274,1280,1282],{},[749,1275,1276,1278],{"accent":617},[606,1277,753],{},[755,1279,757],{},[606,1281,760],{},[603,1283,1284,1286],{},[1263,1285,1265],{},[606,1287,1268],{},[606,1289,1290],{},"P",[610,1292,1293],{"encoding":612},"\\vec{v}_{n+1}^{\\,T} = \\vec{v}_n^{\\,T} P",[587,1295,1297,1420],{"className":1296,"ariaHidden":617},[616],[587,1298,1300,1304,1409,1413,1417],{"className":1299},[621],[587,1301],{"className":1302,"style":1303},[625],"height:1.1478em;vertical-align:-0.3064em;",[587,1305,1307,1342],{"className":1306},[630],[587,1308,1310],{"className":1309},[630,780],[587,1311,1313],{"className":1312},[784],[587,1314,1316],{"className":1315},[788],[587,1317,1319,1327],{"className":1318,"style":793},[792],[587,1320,1321,1324],{"style":796},[587,1322],{"className":1323,"style":801},[800],[587,1325,753],{"className":1326,"style":805},[630,631],[587,1328,1329,1332],{"style":796},[587,1330],{"className":1331,"style":801},[800],[587,1333,1335],{"className":1334,"style":815},[814],[587,1336,1338],{"className":1337,"style":820},[819],[822,1339,1340],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,1341],{"d":833},[587,1343,1345],{"className":1344},[837],[587,1346,1348,1400],{"className":1347},[784,841],[587,1349,1351,1397],{"className":1350},[788],[587,1352,1355,1377],{"className":1353,"style":1354},[792],"height:0.8413em;",[587,1356,1358,1361],{"style":1357},"top:-2.4519em;margin-left:-0.0359em;margin-right:0.05em;",[587,1359],{"className":1360,"style":855},[800],[587,1362,1364],{"className":1363},[859,860,861,862],[587,1365,1367,1370,1374],{"className":1366},[630,862],[587,1368,760],{"className":1369},[630,631,862],[587,1371,1257],{"className":1372},[1373,862],"mbin",[587,1375,712],{"className":1376},[630,862],[587,1378,1379,1382],{"style":992},[587,1380],{"className":1381,"style":855},[800],[587,1383,1385],{"className":1384},[859,860,861,862],[587,1386,1388,1393],{"className":1387},[630,862],[587,1389],{"className":1390,"style":1392},[1391,862],"mspace","margin-right:0.1952em;",[587,1394,1268],{"className":1395,"style":1396},[630,631,862],"margin-right:0.1389em;",[587,1398,870],{"className":1399},[869],[587,1401,1403],{"className":1402},[788],[587,1404,1407],{"className":1405,"style":1406},[792],"height:0.3064em;",[587,1408],{},[587,1410],{"className":1411,"style":1412},[1391],"margin-right:0.2778em;",[587,1414,1271],{"className":1415},[1416],"mrel",[587,1418],{"className":1419,"style":1412},[1391],[587,1421,1423,1427,1518],{"className":1422},[621],[587,1424],{"className":1425,"style":1426},[625],"height:1.0883em;vertical-align:-0.247em;",[587,1428,1430,1465],{"className":1429},[630],[587,1431,1433],{"className":1432},[630,780],[587,1434,1436],{"className":1435},[784],[587,1437,1439],{"className":1438},[788],[587,1440,1442,1450],{"className":1441,"style":793},[792],[587,1443,1444,1447],{"style":796},[587,1445],{"className":1446,"style":801},[800],[587,1448,753],{"className":1449,"style":805},[630,631],[587,1451,1452,1455],{"style":796},[587,1453],{"className":1454,"style":801},[800],[587,1456,1458],{"className":1457,"style":815},[814],[587,1459,1461],{"className":1460,"style":820},[819],[822,1462,1463],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,1464],{"d":833},[587,1466,1468],{"className":1467},[837],[587,1469,1471,1509],{"className":1470},[784,841],[587,1472,1474,1506],{"className":1473},[788],[587,1475,1477,1489],{"className":1476,"style":1354},[792],[587,1478,1480,1483],{"style":1479},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[587,1481],{"className":1482,"style":855},[800],[587,1484,1486],{"className":1485},[859,860,861,862],[587,1487,760],{"className":1488},[630,631,862],[587,1490,1491,1494],{"style":992},[587,1492],{"className":1493,"style":855},[800],[587,1495,1497],{"className":1496},[859,860,861,862],[587,1498,1500,1503],{"className":1499},[630,862],[587,1501],{"className":1502,"style":1392},[1391,862],[587,1504,1268],{"className":1505,"style":1396},[630,631,862],[587,1507,870],{"className":1508},[869],[587,1510,1512],{"className":1511},[788],[587,1513,1516],{"className":1514,"style":1515},[792],"height:0.247em;",[587,1517],{},[587,1519,1290],{"className":1520,"style":1396},[630,631],". Dann ist ",[587,1523,1525,1547],{"className":1524},[590],[587,1526,1528],{"className":1527},[594],[596,1529,1530],{"xmlns":598},[600,1531,1532,1544],{},[603,1533,1534,1536,1538],{},[606,1535,1290],{},[755,1537,1271],{},[953,1539,1540,1542],{},[606,1541,608],{},[606,1543,1268],{},[610,1545,1546],{"encoding":612},"P = A^T",[587,1548,1550,1568],{"className":1549,"ariaHidden":617},[616],[587,1551,1553,1556,1559,1562,1565],{"className":1552},[621],[587,1554],{"className":1555,"style":626},[625],[587,1557,1290],{"className":1558,"style":1396},[630,631],[587,1560],{"className":1561,"style":1412},[1391],[587,1563,1271],{"className":1564},[1416],[587,1566],{"className":1567,"style":1412},[1391],[587,1569,1571,1574],{"className":1570},[621],[587,1572],{"className":1573,"style":1354},[625],[587,1575,1577,1580],{"className":1576},[630],[587,1578,608],{"className":1579},[630,631],[587,1581,1583],{"className":1582},[837],[587,1584,1586],{"className":1585},[784],[587,1587,1589],{"className":1588},[788],[587,1590,1592],{"className":1591,"style":1354},[792],[587,1593,1594,1597],{"style":992},[587,1595],{"className":1596,"style":855},[800],[587,1598,1600],{"className":1599},[859,860,861,862],[587,1601,1268],{"className":1602,"style":1396},[630,631,862],", und die Zeilensummen sind ",[587,1605,1607,1620],{"className":1606},[590],[587,1608,1610],{"className":1609},[594],[596,1611,1612],{"xmlns":598},[600,1613,1614,1618],{},[603,1615,1616],{},[710,1617,712],{},[610,1619,712],{"encoding":612},[587,1621,1623],{"className":1622,"ariaHidden":617},[616],[587,1624,1626,1629],{"className":1625},[621],[587,1627],{"className":1628,"style":724},[625],[587,1630,712],{"className":1631},[630],[560,1633,1635],{"id":1634},"beispiele","Beispiele",[565,1637,1638,1639,1683,1684,1724,1725,1683,1765,1805],{},"Zwei Mobilfunkanbieter X und Y: Von den Kunden von X bleiben pro Jahr ",[587,1640,1642,1663],{"className":1641},[590],[587,1643,1645],{"className":1644},[594],[596,1646,1647],{"xmlns":598},[600,1648,1649,1660],{},[603,1650,1651,1654,1656],{},[710,1652,1653],{},"80",[1263,1655,1265],{},[606,1657,1659],{"mathvariant":1658},"normal","%",[610,1661,1662],{"encoding":612},"80\\,\\%",[587,1664,1666],{"className":1665,"ariaHidden":617},[616],[587,1667,1669,1673,1676,1680],{"className":1668},[621],[587,1670],{"className":1671,"style":1672},[625],"height:0.8056em;vertical-align:-0.0556em;",[587,1674,1653],{"className":1675},[630],[587,1677],{"className":1678,"style":1679},[1391],"margin-right:0.1667em;",[587,1681,1659],{"className":1682},[630],", ",[587,1685,1687,1706],{"className":1686},[590],[587,1688,1690],{"className":1689},[594],[596,1691,1692],{"xmlns":598},[600,1693,1694,1703],{},[603,1695,1696,1699,1701],{},[710,1697,1698],{},"20",[1263,1700,1265],{},[606,1702,1659],{"mathvariant":1658},[610,1704,1705],{"encoding":612},"20\\,\\%",[587,1707,1709],{"className":1708,"ariaHidden":617},[616],[587,1710,1712,1715,1718,1721],{"className":1711},[621],[587,1713],{"className":1714,"style":1672},[625],[587,1716,1698],{"className":1717},[630],[587,1719],{"className":1720,"style":1679},[1391],[587,1722,1659],{"className":1723},[630]," wechseln zu Y. Von Y bleiben ",[587,1726,1728,1747],{"className":1727},[590],[587,1729,1731],{"className":1730},[594],[596,1732,1733],{"xmlns":598},[600,1734,1735,1744],{},[603,1736,1737,1740,1742],{},[710,1738,1739],{},"70",[1263,1741,1265],{},[606,1743,1659],{"mathvariant":1658},[610,1745,1746],{"encoding":612},"70\\,\\%",[587,1748,1750],{"className":1749,"ariaHidden":617},[616],[587,1751,1753,1756,1759,1762],{"className":1752},[621],[587,1754],{"className":1755,"style":1672},[625],[587,1757,1739],{"className":1758},[630],[587,1760],{"className":1761,"style":1679},[1391],[587,1763,1659],{"className":1764},[630],[587,1766,1768,1787],{"className":1767},[590],[587,1769,1771],{"className":1770},[594],[596,1772,1773],{"xmlns":598},[600,1774,1775,1784],{},[603,1776,1777,1780,1782],{},[710,1778,1779],{},"30",[1263,1781,1265],{},[606,1783,1659],{"mathvariant":1658},[610,1785,1786],{"encoding":612},"30\\,\\%",[587,1788,1790],{"className":1789,"ariaHidden":617},[616],[587,1791,1793,1796,1799,1802],{"className":1792},[621],[587,1794],{"className":1795,"style":1672},[625],[587,1797,1779],{"className":1798},[630],[587,1800],{"className":1801,"style":1679},[1391],[587,1803,1659],{"className":1804},[630]," wechseln zu X. Mit der Reihenfolge (X, Y):",[587,1807,1810],{"className":1808},[1809],"katex-display",[587,1811,1813,1878],{"className":1812},[590],[587,1814,1816],{"className":1815},[594],[596,1817,1819],{"xmlns":598,"display":1818},"block",[600,1820,1821,1875],{},[603,1822,1823,1825,1827],{},[606,1824,608],{},[755,1826,1271],{},[603,1828,1829,1831,1873],{},[755,1830,1021],{"fence":617},[1832,1833,1837,1857],"mtable",{"rowspacing":1834,"columnalign":1835,"columnspacing":1836},"0.16em","center center","1em",[1838,1839,1840,1850],"mtr",{},[1841,1842,1843],"mtd",{},[1844,1845,1847],"mstyle",{"scriptlevel":1846,"displaystyle":1020},"0",[710,1848,1849],{},"0,8",[1841,1851,1852],{},[1844,1853,1854],{"scriptlevel":1846,"displaystyle":1020},[710,1855,1856],{},"0,3",[1838,1858,1859,1866],{},[1841,1860,1861],{},[1844,1862,1863],{"scriptlevel":1846,"displaystyle":1020},[710,1864,1865],{},"0,2",[1841,1867,1868],{},[1844,1869,1870],{"scriptlevel":1846,"displaystyle":1020},[710,1871,1872],{},"0,7",[755,1874,1032],{"fence":617},[610,1876,1877],{"encoding":612},"A = \\begin{pmatrix} 0{,}8 & 0{,}3 \\\\ 0{,}2 & 0{,}7 \\end{pmatrix}",[587,1879,1881,1899],{"className":1880,"ariaHidden":617},[616],[587,1882,1884,1887,1890,1893,1896],{"className":1883},[621],[587,1885],{"className":1886,"style":626},[625],[587,1888,608],{"className":1889},[630,631],[587,1891],{"className":1892,"style":1412},[1391],[587,1894,1271],{"className":1895},[1416],[587,1897],{"className":1898,"style":1412},[1391],[587,1900,1902,1906],{"className":1901},[621],[587,1903],{"className":1904,"style":1905},[625],"height:2.4em;vertical-align:-0.95em;",[587,1907,1910,1919,2070],{"className":1908},[1909],"minner",[587,1911,1915],{"className":1912,"style":1914},[1056,1913],"delimcenter","top:0em;",[587,1916,1021],{"className":1917},[1918,861],"delimsizing",[587,1920,1922],{"className":1921},[630],[587,1923,1925,1997,2002,2005],{"className":1924},[1832],[587,1926,1929],{"className":1927},[1928],"col-align-c",[587,1930,1932,1988],{"className":1931},[784,841],[587,1933,1935,1985],{"className":1934},[788],[587,1936,1939,1963],{"className":1937,"style":1938},[792],"height:1.45em;",[587,1940,1942,1945],{"style":1941},"top:-3.61em;",[587,1943],{"className":1944,"style":801},[800],[587,1946,1948,1951,1959],{"className":1947},[630],[587,1949,1846],{"className":1950},[630],[587,1952,1954],{"className":1953},[630],[587,1955,1958],{"className":1956},[1957],"mpunct",",",[587,1960,1962],{"className":1961},[630],"8",[587,1964,1966,1969],{"style":1965},"top:-2.41em;",[587,1967],{"className":1968,"style":801},[800],[587,1970,1972,1975,1981],{"className":1971},[630],[587,1973,1846],{"className":1974},[630],[587,1976,1978],{"className":1977},[630],[587,1979,1958],{"className":1980},[1957],[587,1982,1984],{"className":1983},[630],"2",[587,1986,870],{"className":1987},[869],[587,1989,1991],{"className":1990},[788],[587,1992,1995],{"className":1993,"style":1994},[792],"height:0.95em;",[587,1996],{},[587,1998],{"className":1999,"style":2001},[2000],"arraycolsep","width:0.5em;",[587,2003],{"className":2004,"style":2001},[2000],[587,2006,2008],{"className":2007},[1928],[587,2009,2011,2062],{"className":2010},[784,841],[587,2012,2014,2059],{"className":2013},[788],[587,2015,2017,2038],{"className":2016,"style":1938},[792],[587,2018,2019,2022],{"style":1941},[587,2020],{"className":2021,"style":801},[800],[587,2023,2025,2028,2034],{"className":2024},[630],[587,2026,1846],{"className":2027},[630],[587,2029,2031],{"className":2030},[630],[587,2032,1958],{"className":2033},[1957],[587,2035,2037],{"className":2036},[630],"3",[587,2039,2040,2043],{"style":1965},[587,2041],{"className":2042,"style":801},[800],[587,2044,2046,2049,2055],{"className":2045},[630],[587,2047,1846],{"className":2048},[630],[587,2050,2052],{"className":2051},[630],[587,2053,1958],{"className":2054},[1957],[587,2056,2058],{"className":2057},[630],"7",[587,2060,870],{"className":2061},[869],[587,2063,2065],{"className":2064},[788],[587,2066,2068],{"className":2067,"style":1994},[792],[587,2069],{},[587,2071,2073],{"className":2072,"style":1914},[1089,1913],[587,2074,1032],{"className":2075},[1918,861],[565,2077,2078,2079,2119],{},"Zu Beginn haben beide je ",[587,2080,2082,2101],{"className":2081},[590],[587,2083,2085],{"className":2084},[594],[596,2086,2087],{"xmlns":598},[600,2088,2089,2098],{},[603,2090,2091,2094,2096],{},[710,2092,2093],{},"50",[1263,2095,1265],{},[606,2097,1659],{"mathvariant":1658},[610,2099,2100],{"encoding":612},"50\\,\\%",[587,2102,2104],{"className":2103,"ariaHidden":617},[616],[587,2105,2107,2110,2113,2116],{"className":2106},[621],[587,2108],{"className":2109,"style":1672},[625],[587,2111,2093],{"className":2112},[630],[587,2114],{"className":2115,"style":1679},[1391],[587,2117,1659],{"className":2118},[630]," Marktanteil:",[587,2121,2123],{"className":2122},[1809],[587,2124,2126,2300],{"className":2125},[590],[587,2127,2129],{"className":2128},[594],[596,2130,2131],{"xmlns":598,"display":1818},[600,2132,2133,2297],{},[603,2134,2135,2145,2147,2183,2209,2211,2237,2239,2242,2252,2254,2256,2259,2269,2271],{},[746,2136,2137,2143],{},[749,2138,2139,2141],{"accent":617},[606,2140,753],{},[755,2142,757],{},[710,2144,712],{},[755,2146,1271],{},[603,2148,2149,2151,2181],{},[755,2150,1021],{"fence":617},[1832,2152,2153,2167],{"rowspacing":1834,"columnalign":1835,"columnspacing":1836},[1838,2154,2155,2161],{},[1841,2156,2157],{},[1844,2158,2159],{"scriptlevel":1846,"displaystyle":1020},[710,2160,1849],{},[1841,2162,2163],{},[1844,2164,2165],{"scriptlevel":1846,"displaystyle":1020},[710,2166,1856],{},[1838,2168,2169,2175],{},[1841,2170,2171],{},[1844,2172,2173],{"scriptlevel":1846,"displaystyle":1020},[710,2174,1865],{},[1841,2176,2177],{},[1844,2178,2179],{"scriptlevel":1846,"displaystyle":1020},[710,2180,1872],{},[755,2182,1032],{"fence":617},[603,2184,2185,2187,2207],{},[755,2186,1021],{"fence":617},[1832,2188,2190,2199],{"rowspacing":1834,"columnalign":2189,"columnspacing":1836},"center",[1838,2191,2192],{},[1841,2193,2194],{},[1844,2195,2196],{"scriptlevel":1846,"displaystyle":1020},[710,2197,2198],{},"0,5",[1838,2200,2201],{},[1841,2202,2203],{},[1844,2204,2205],{"scriptlevel":1846,"displaystyle":1020},[710,2206,2198],{},[755,2208,1032],{"fence":617},[755,2210,1271],{},[603,2212,2213,2215,2235],{},[755,2214,1021],{"fence":617},[1832,2216,2217,2226],{"rowspacing":1834,"columnalign":2189,"columnspacing":1836},[1838,2218,2219],{},[1841,2220,2221],{},[1844,2222,2223],{"scriptlevel":1846,"displaystyle":1020},[710,2224,2225],{},"0,55",[1838,2227,2228],{},[1841,2229,2230],{},[1844,2231,2232],{"scriptlevel":1846,"displaystyle":1020},[710,2233,2234],{},"0,45",[755,2236,1032],{"fence":617},[755,2238,1958],{"separator":617},[1391,2240],{"width":2241},"2em",[746,2243,2244,2250],{},[749,2245,2246,2248],{"accent":617},[606,2247,753],{},[755,2249,757],{},[710,2251,1984],{},[755,2253,1271],{},[606,2255,608],{},[755,2257,2258],{},"⋅",[746,2260,2261,2267],{},[749,2262,2263,2265],{"accent":617},[606,2264,753],{},[755,2266,757],{},[710,2268,712],{},[755,2270,1271],{},[603,2272,2273,2275,2295],{},[755,2274,1021],{"fence":617},[1832,2276,2277,2286],{"rowspacing":1834,"columnalign":2189,"columnspacing":1836},[1838,2278,2279],{},[1841,2280,2281],{},[1844,2282,2283],{"scriptlevel":1846,"displaystyle":1020},[710,2284,2285],{},"0,575",[1838,2287,2288],{},[1841,2289,2290],{},[1844,2291,2292],{"scriptlevel":1846,"displaystyle":1020},[710,2293,2294],{},"0,425",[755,2296,1032],{"fence":617},[610,2298,2299],{"encoding":612},"\\vec{v}_1 = \\begin{pmatrix} 0{,}8 & 0{,}3 \\\\ 0{,}2 & 0{,}7 \\end{pmatrix} \\begin{pmatrix} 0{,}5 \\\\ 0{,}5 \\end{pmatrix} = \\begin{pmatrix} 0{,}55 \\\\ 0{,}45 \\end{pmatrix}, \\qquad \\vec{v}_2 = A \\cdot \\vec{v}_1 = \\begin{pmatrix} 0{,}575 \\\\ 0{,}425 \\end{pmatrix}",[587,2301,2303,2391,2647,2833,2852,2939],{"className":2302,"ariaHidden":617},[616],[587,2304,2306,2309,2382,2385,2388],{"className":2305},[621],[587,2307],{"className":2308,"style":773},[625],[587,2310,2312,2347],{"className":2311},[630],[587,2313,2315],{"className":2314},[630,780],[587,2316,2318],{"className":2317},[784],[587,2319,2321],{"className":2320},[788],[587,2322,2324,2332],{"className":2323,"style":793},[792],[587,2325,2326,2329],{"style":796},[587,2327],{"className":2328,"style":801},[800],[587,2330,753],{"className":2331,"style":805},[630,631],[587,2333,2334,2337],{"style":796},[587,2335],{"className":2336,"style":801},[800],[587,2338,2340],{"className":2339,"style":815},[814],[587,2341,2343],{"className":2342,"style":820},[819],[822,2344,2345],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,2346],{"d":833},[587,2348,2350],{"className":2349},[837],[587,2351,2353,2374],{"className":2352},[784,841],[587,2354,2356,2371],{"className":2355},[788],[587,2357,2360],{"className":2358,"style":2359},[792],"height:0.3011em;",[587,2361,2362,2365],{"style":851},[587,2363],{"className":2364,"style":855},[800],[587,2366,2368],{"className":2367},[859,860,861,862],[587,2369,712],{"className":2370},[630,862],[587,2372,870],{"className":2373},[869],[587,2375,2377],{"className":2376},[788],[587,2378,2380],{"className":2379,"style":877},[792],[587,2381],{},[587,2383],{"className":2384,"style":1412},[1391],[587,2386,1271],{"className":2387},[1416],[587,2389],{"className":2390,"style":1412},[1391],[587,2392,2394,2397,2550,2553,2638,2641,2644],{"className":2393},[621],[587,2395],{"className":2396,"style":1905},[625],[587,2398,2400,2406,2544],{"className":2399},[1909],[587,2401,2403],{"className":2402,"style":1914},[1056,1913],[587,2404,1021],{"className":2405},[1918,861],[587,2407,2409],{"className":2408},[630],[587,2410,2412,2475,2478,2481],{"className":2411},[1832],[587,2413,2415],{"className":2414},[1928],[587,2416,2418,2467],{"className":2417},[784,841],[587,2419,2421,2464],{"className":2420},[788],[587,2422,2424,2444],{"className":2423,"style":1938},[792],[587,2425,2426,2429],{"style":1941},[587,2427],{"className":2428,"style":801},[800],[587,2430,2432,2435,2441],{"className":2431},[630],[587,2433,1846],{"className":2434},[630],[587,2436,2438],{"className":2437},[630],[587,2439,1958],{"className":2440},[1957],[587,2442,1962],{"className":2443},[630],[587,2445,2446,2449],{"style":1965},[587,2447],{"className":2448,"style":801},[800],[587,2450,2452,2455,2461],{"className":2451},[630],[587,2453,1846],{"className":2454},[630],[587,2456,2458],{"className":2457},[630],[587,2459,1958],{"className":2460},[1957],[587,2462,1984],{"className":2463},[630],[587,2465,870],{"className":2466},[869],[587,2468,2470],{"className":2469},[788],[587,2471,2473],{"className":2472,"style":1994},[792],[587,2474],{},[587,2476],{"className":2477,"style":2001},[2000],[587,2479],{"className":2480,"style":2001},[2000],[587,2482,2484],{"className":2483},[1928],[587,2485,2487,2536],{"className":2486},[784,841],[587,2488,2490,2533],{"className":2489},[788],[587,2491,2493,2513],{"className":2492,"style":1938},[792],[587,2494,2495,2498],{"style":1941},[587,2496],{"className":2497,"style":801},[800],[587,2499,2501,2504,2510],{"className":2500},[630],[587,2502,1846],{"className":2503},[630],[587,2505,2507],{"className":2506},[630],[587,2508,1958],{"className":2509},[1957],[587,2511,2037],{"className":2512},[630],[587,2514,2515,2518],{"style":1965},[587,2516],{"className":2517,"style":801},[800],[587,2519,2521,2524,2530],{"className":2520},[630],[587,2522,1846],{"className":2523},[630],[587,2525,2527],{"className":2526},[630],[587,2528,1958],{"className":2529},[1957],[587,2531,2058],{"className":2532},[630],[587,2534,870],{"className":2535},[869],[587,2537,2539],{"className":2538},[788],[587,2540,2542],{"className":2541,"style":1994},[792],[587,2543],{},[587,2545,2547],{"className":2546,"style":1914},[1089,1913],[587,2548,1032],{"className":2549},[1918,861],[587,2551],{"className":2552,"style":1679},[1391],[587,2554,2556,2562,2632],{"className":2555},[1909],[587,2557,2559],{"className":2558,"style":1914},[1056,1913],[587,2560,1021],{"className":2561},[1918,861],[587,2563,2565],{"className":2564},[630],[587,2566,2568],{"className":2567},[1832],[587,2569,2571],{"className":2570},[1928],[587,2572,2574,2624],{"className":2573},[784,841],[587,2575,2577,2621],{"className":2576},[788],[587,2578,2580,2601],{"className":2579,"style":1938},[792],[587,2581,2582,2585],{"style":1941},[587,2583],{"className":2584,"style":801},[800],[587,2586,2588,2591,2597],{"className":2587},[630],[587,2589,1846],{"className":2590},[630],[587,2592,2594],{"className":2593},[630],[587,2595,1958],{"className":2596},[1957],[587,2598,2600],{"className":2599},[630],"5",[587,2602,2603,2606],{"style":1965},[587,2604],{"className":2605,"style":801},[800],[587,2607,2609,2612,2618],{"className":2608},[630],[587,2610,1846],{"className":2611},[630],[587,2613,2615],{"className":2614},[630],[587,2616,1958],{"className":2617},[1957],[587,2619,2600],{"className":2620},[630],[587,2622,870],{"className":2623},[869],[587,2625,2627],{"className":2626},[788],[587,2628,2630],{"className":2629,"style":1994},[792],[587,2631],{},[587,2633,2635],{"className":2634,"style":1914},[1089,1913],[587,2636,1032],{"className":2637},[1918,861],[587,2639],{"className":2640,"style":1412},[1391],[587,2642,1271],{"className":2643},[1416],[587,2645],{"className":2646,"style":1412},[1391],[587,2648,2650,2653,2739,2742,2745,2749,2752,2824,2827,2830],{"className":2649},[621],[587,2651],{"className":2652,"style":1905},[625],[587,2654,2656,2662,2733],{"className":2655},[1909],[587,2657,2659],{"className":2658,"style":1914},[1056,1913],[587,2660,1021],{"className":2661},[1918,861],[587,2663,2665],{"className":2664},[630],[587,2666,2668],{"className":2667},[1832],[587,2669,2671],{"className":2670},[1928],[587,2672,2674,2725],{"className":2673},[784,841],[587,2675,2677,2722],{"className":2676},[788],[587,2678,2680,2701],{"className":2679,"style":1938},[792],[587,2681,2682,2685],{"style":1941},[587,2683],{"className":2684,"style":801},[800],[587,2686,2688,2691,2697],{"className":2687},[630],[587,2689,1846],{"className":2690},[630],[587,2692,2694],{"className":2693},[630],[587,2695,1958],{"className":2696},[1957],[587,2698,2700],{"className":2699},[630],"55",[587,2702,2703,2706],{"style":1965},[587,2704],{"className":2705,"style":801},[800],[587,2707,2709,2712,2718],{"className":2708},[630],[587,2710,1846],{"className":2711},[630],[587,2713,2715],{"className":2714},[630],[587,2716,1958],{"className":2717},[1957],[587,2719,2721],{"className":2720},[630],"45",[587,2723,870],{"className":2724},[869],[587,2726,2728],{"className":2727},[788],[587,2729,2731],{"className":2730,"style":1994},[792],[587,2732],{},[587,2734,2736],{"className":2735,"style":1914},[1089,1913],[587,2737,1032],{"className":2738},[1918,861],[587,2740],{"className":2741,"style":1679},[1391],[587,2743,1958],{"className":2744},[1957],[587,2746],{"className":2747,"style":2748},[1391],"margin-right:2em;",[587,2750],{"className":2751,"style":1679},[1391],[587,2753,2755,2790],{"className":2754},[630],[587,2756,2758],{"className":2757},[630,780],[587,2759,2761],{"className":2760},[784],[587,2762,2764],{"className":2763},[788],[587,2765,2767,2775],{"className":2766,"style":793},[792],[587,2768,2769,2772],{"style":796},[587,2770],{"className":2771,"style":801},[800],[587,2773,753],{"className":2774,"style":805},[630,631],[587,2776,2777,2780],{"style":796},[587,2778],{"className":2779,"style":801},[800],[587,2781,2783],{"className":2782,"style":815},[814],[587,2784,2786],{"className":2785,"style":820},[819],[822,2787,2788],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,2789],{"d":833},[587,2791,2793],{"className":2792},[837],[587,2794,2796,2816],{"className":2795},[784,841],[587,2797,2799,2813],{"className":2798},[788],[587,2800,2802],{"className":2801,"style":2359},[792],[587,2803,2804,2807],{"style":851},[587,2805],{"className":2806,"style":855},[800],[587,2808,2810],{"className":2809},[859,860,861,862],[587,2811,1984],{"className":2812},[630,862],[587,2814,870],{"className":2815},[869],[587,2817,2819],{"className":2818},[788],[587,2820,2822],{"className":2821,"style":877},[792],[587,2823],{},[587,2825],{"className":2826,"style":1412},[1391],[587,2828,1271],{"className":2829},[1416],[587,2831],{"className":2832,"style":1412},[1391],[587,2834,2836,2839,2842,2846,2849],{"className":2835},[621],[587,2837],{"className":2838,"style":626},[625],[587,2840,608],{"className":2841},[630,631],[587,2843],{"className":2844,"style":2845},[1391],"margin-right:0.2222em;",[587,2847,2258],{"className":2848},[1373],[587,2850],{"className":2851,"style":2845},[1391],[587,2853,2855,2858,2930,2933,2936],{"className":2854},[621],[587,2856],{"className":2857,"style":773},[625],[587,2859,2861,2896],{"className":2860},[630],[587,2862,2864],{"className":2863},[630,780],[587,2865,2867],{"className":2866},[784],[587,2868,2870],{"className":2869},[788],[587,2871,2873,2881],{"className":2872,"style":793},[792],[587,2874,2875,2878],{"style":796},[587,2876],{"className":2877,"style":801},[800],[587,2879,753],{"className":2880,"style":805},[630,631],[587,2882,2883,2886],{"style":796},[587,2884],{"className":2885,"style":801},[800],[587,2887,2889],{"className":2888,"style":815},[814],[587,2890,2892],{"className":2891,"style":820},[819],[822,2893,2894],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,2895],{"d":833},[587,2897,2899],{"className":2898},[837],[587,2900,2902,2922],{"className":2901},[784,841],[587,2903,2905,2919],{"className":2904},[788],[587,2906,2908],{"className":2907,"style":2359},[792],[587,2909,2910,2913],{"style":851},[587,2911],{"className":2912,"style":855},[800],[587,2914,2916],{"className":2915},[859,860,861,862],[587,2917,712],{"className":2918},[630,862],[587,2920,870],{"className":2921},[869],[587,2923,2925],{"className":2924},[788],[587,2926,2928],{"className":2927,"style":877},[792],[587,2929],{},[587,2931],{"className":2932,"style":1412},[1391],[587,2934,1271],{"className":2935},[1416],[587,2937],{"className":2938,"style":1412},[1391],[587,2940,2942,2945],{"className":2941},[621],[587,2943],{"className":2944,"style":1905},[625],[587,2946,2948,2954,3025],{"className":2947},[1909],[587,2949,2951],{"className":2950,"style":1914},[1056,1913],[587,2952,1021],{"className":2953},[1918,861],[587,2955,2957],{"className":2956},[630],[587,2958,2960],{"className":2959},[1832],[587,2961,2963],{"className":2962},[1928],[587,2964,2966,3017],{"className":2965},[784,841],[587,2967,2969,3014],{"className":2968},[788],[587,2970,2972,2993],{"className":2971,"style":1938},[792],[587,2973,2974,2977],{"style":1941},[587,2975],{"className":2976,"style":801},[800],[587,2978,2980,2983,2989],{"className":2979},[630],[587,2981,1846],{"className":2982},[630],[587,2984,2986],{"className":2985},[630],[587,2987,1958],{"className":2988},[1957],[587,2990,2992],{"className":2991},[630],"575",[587,2994,2995,2998],{"style":1965},[587,2996],{"className":2997,"style":801},[800],[587,2999,3001,3004,3010],{"className":3000},[630],[587,3002,1846],{"className":3003},[630],[587,3005,3007],{"className":3006},[630],[587,3008,1958],{"className":3009},[1957],[587,3011,3013],{"className":3012},[630],"425",[587,3015,870],{"className":3016},[869],[587,3018,3020],{"className":3019},[788],[587,3021,3023],{"className":3022,"style":1994},[792],[587,3024],{},[587,3026,3028],{"className":3027,"style":1914},[1089,1913],[587,3029,1032],{"className":3030},[1918,861],[565,3032,3033,3034,3193,3194,1002],{},"Dasselbe Ergebnis liefert ",[587,3035,3037,3067],{"className":3036},[590],[587,3038,3040],{"className":3039},[594],[596,3041,3042],{"xmlns":598},[600,3043,3044,3064],{},[603,3045,3046,3052,3054],{},[953,3047,3048,3050],{},[606,3049,608],{},[710,3051,1984],{},[755,3053,2258],{},[746,3055,3056,3062],{},[749,3057,3058,3060],{"accent":617},[606,3059,753],{},[755,3061,757],{},[710,3063,1846],{},[610,3065,3066],{"encoding":612},"A^2 \\cdot \\vec{v}_0",[587,3068,3070,3115],{"className":3069,"ariaHidden":617},[616],[587,3071,3073,3077,3106,3109,3112],{"className":3072},[621],[587,3074],{"className":3075,"style":3076},[625],"height:0.8141em;",[587,3078,3080,3083],{"className":3079},[630],[587,3081,608],{"className":3082},[630,631],[587,3084,3086],{"className":3085},[837],[587,3087,3089],{"className":3088},[784],[587,3090,3092],{"className":3091},[788],[587,3093,3095],{"className":3094,"style":3076},[792],[587,3096,3097,3100],{"style":992},[587,3098],{"className":3099,"style":855},[800],[587,3101,3103],{"className":3102},[859,860,861,862],[587,3104,1984],{"className":3105},[630,862],[587,3107],{"className":3108,"style":2845},[1391],[587,3110,2258],{"className":3111},[1373],[587,3113],{"className":3114,"style":2845},[1391],[587,3116,3118,3121],{"className":3117},[621],[587,3119],{"className":3120,"style":773},[625],[587,3122,3124,3159],{"className":3123},[630],[587,3125,3127],{"className":3126},[630,780],[587,3128,3130],{"className":3129},[784],[587,3131,3133],{"className":3132},[788],[587,3134,3136,3144],{"className":3135,"style":793},[792],[587,3137,3138,3141],{"style":796},[587,3139],{"className":3140,"style":801},[800],[587,3142,753],{"className":3143,"style":805},[630,631],[587,3145,3146,3149],{"style":796},[587,3147],{"className":3148,"style":801},[800],[587,3150,3152],{"className":3151,"style":815},[814],[587,3153,3155],{"className":3154,"style":820},[819],[822,3156,3157],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,3158],{"d":833},[587,3160,3162],{"className":3161},[837],[587,3163,3165,3185],{"className":3164},[784,841],[587,3166,3168,3182],{"className":3167},[788],[587,3169,3171],{"className":3170,"style":2359},[792],[587,3172,3173,3176],{"style":851},[587,3174],{"className":3175,"style":855},[800],[587,3177,3179],{"className":3178},[859,860,861,862],[587,3180,1846],{"className":3181},[630,862],[587,3183,870],{"className":3184},[869],[587,3186,3188],{"className":3187},[788],[587,3189,3191],{"className":3190,"style":877},[792],[587,3192],{}," mit ",[587,3195,3197,3253],{"className":3196},[590],[587,3198,3200],{"className":3199},[594],[596,3201,3202],{"xmlns":598},[600,3203,3204,3250],{},[603,3205,3206,3212,3214],{},[953,3207,3208,3210],{},[606,3209,608],{},[710,3211,1984],{},[755,3213,1271],{},[603,3215,3216,3218,3248],{},[755,3217,1021],{"fence":617},[1832,3219,3220,3234],{"rowspacing":1834,"columnalign":1835,"columnspacing":1836},[1838,3221,3222,3228],{},[1841,3223,3224],{},[1844,3225,3226],{"scriptlevel":1846,"displaystyle":1020},[710,3227,1872],{},[1841,3229,3230],{},[1844,3231,3232],{"scriptlevel":1846,"displaystyle":1020},[710,3233,2234],{},[1838,3235,3236,3242],{},[1841,3237,3238],{},[1844,3239,3240],{"scriptlevel":1846,"displaystyle":1020},[710,3241,1856],{},[1841,3243,3244],{},[1844,3245,3246],{"scriptlevel":1846,"displaystyle":1020},[710,3247,2225],{},[755,3249,1032],{"fence":617},[610,3251,3252],{"encoding":612},"A^2 = \\begin{pmatrix} 0{,}7 & 0{,}45 \\\\ 0{,}3 & 0{,}55 \\end{pmatrix}",[587,3254,3256,3300],{"className":3255,"ariaHidden":617},[616],[587,3257,3259,3262,3291,3294,3297],{"className":3258},[621],[587,3260],{"className":3261,"style":3076},[625],[587,3263,3265,3268],{"className":3264},[630],[587,3266,608],{"className":3267},[630,631],[587,3269,3271],{"className":3270},[837],[587,3272,3274],{"className":3273},[784],[587,3275,3277],{"className":3276},[788],[587,3278,3280],{"className":3279,"style":3076},[792],[587,3281,3282,3285],{"style":992},[587,3283],{"className":3284,"style":855},[800],[587,3286,3288],{"className":3287},[859,860,861,862],[587,3289,1984],{"className":3290},[630,862],[587,3292],{"className":3293,"style":1412},[1391],[587,3295,1271],{"className":3296},[1416],[587,3298],{"className":3299,"style":1412},[1391],[587,3301,3303,3306],{"className":3302},[621],[587,3304],{"className":3305,"style":1905},[625],[587,3307,3309,3315,3453],{"className":3308},[1909],[587,3310,3312],{"className":3311,"style":1914},[1056,1913],[587,3313,1021],{"className":3314},[1918,861],[587,3316,3318],{"className":3317},[630],[587,3319,3321,3384,3387,3390],{"className":3320},[1832],[587,3322,3324],{"className":3323},[1928],[587,3325,3327,3376],{"className":3326},[784,841],[587,3328,3330,3373],{"className":3329},[788],[587,3331,3333,3353],{"className":3332,"style":1938},[792],[587,3334,3335,3338],{"style":1941},[587,3336],{"className":3337,"style":801},[800],[587,3339,3341,3344,3350],{"className":3340},[630],[587,3342,1846],{"className":3343},[630],[587,3345,3347],{"className":3346},[630],[587,3348,1958],{"className":3349},[1957],[587,3351,2058],{"className":3352},[630],[587,3354,3355,3358],{"style":1965},[587,3356],{"className":3357,"style":801},[800],[587,3359,3361,3364,3370],{"className":3360},[630],[587,3362,1846],{"className":3363},[630],[587,3365,3367],{"className":3366},[630],[587,3368,1958],{"className":3369},[1957],[587,3371,2037],{"className":3372},[630],[587,3374,870],{"className":3375},[869],[587,3377,3379],{"className":3378},[788],[587,3380,3382],{"className":3381,"style":1994},[792],[587,3383],{},[587,3385],{"className":3386,"style":2001},[2000],[587,3388],{"className":3389,"style":2001},[2000],[587,3391,3393],{"className":3392},[1928],[587,3394,3396,3445],{"className":3395},[784,841],[587,3397,3399,3442],{"className":3398},[788],[587,3400,3402,3422],{"className":3401,"style":1938},[792],[587,3403,3404,3407],{"style":1941},[587,3405],{"className":3406,"style":801},[800],[587,3408,3410,3413,3419],{"className":3409},[630],[587,3411,1846],{"className":3412},[630],[587,3414,3416],{"className":3415},[630],[587,3417,1958],{"className":3418},[1957],[587,3420,2721],{"className":3421},[630],[587,3423,3424,3427],{"style":1965},[587,3425],{"className":3426,"style":801},[800],[587,3428,3430,3433,3439],{"className":3429},[630],[587,3431,1846],{"className":3432},[630],[587,3434,3436],{"className":3435},[630],[587,3437,1958],{"className":3438},[1957],[587,3440,2700],{"className":3441},[630],[587,3443,870],{"className":3444},[869],[587,3446,3448],{"className":3447},[788],[587,3449,3451],{"className":3450,"style":1994},[792],[587,3452],{},[587,3454,3456],{"className":3455,"style":1914},[1089,1913],[587,3457,1032],{"className":3458},[1918,861],[565,3460,3461,3462,1002],{},"Ein Kunde von X wechselt im ersten Jahr zu Y, im zweiten zurück zu X und bleibt im dritten Jahr bei X. Die Wahrscheinlichkeit für genau diesen Pfad ist ",[587,3463,3465,3492],{"className":3464},[590],[587,3466,3468],{"className":3467},[594],[596,3469,3470],{"xmlns":598},[600,3471,3472,3489],{},[603,3473,3474,3476,3478,3480,3482,3484,3486],{},[710,3475,1865],{},[755,3477,2258],{},[710,3479,1856],{},[755,3481,2258],{},[710,3483,1849],{},[755,3485,1271],{},[710,3487,3488],{},"0,048",[610,3490,3491],{"encoding":612},"0{,}2 \\cdot 0{,}3 \\cdot 0{,}8 = 0{,}048",[587,3493,3495,3523,3550,3577],{"className":3494,"ariaHidden":617},[616],[587,3496,3498,3502,3505,3511,3514,3517,3520],{"className":3497},[621],[587,3499],{"className":3500,"style":3501},[625],"height:0.8389em;vertical-align:-0.1944em;",[587,3503,1846],{"className":3504},[630],[587,3506,3508],{"className":3507},[630],[587,3509,1958],{"className":3510},[1957],[587,3512,1984],{"className":3513},[630],[587,3515],{"className":3516,"style":2845},[1391],[587,3518,2258],{"className":3519},[1373],[587,3521],{"className":3522,"style":2845},[1391],[587,3524,3526,3529,3532,3538,3541,3544,3547],{"className":3525},[621],[587,3527],{"className":3528,"style":3501},[625],[587,3530,1846],{"className":3531},[630],[587,3533,3535],{"className":3534},[630],[587,3536,1958],{"className":3537},[1957],[587,3539,2037],{"className":3540},[630],[587,3542],{"className":3543,"style":2845},[1391],[587,3545,2258],{"className":3546},[1373],[587,3548],{"className":3549,"style":2845},[1391],[587,3551,3553,3556,3559,3565,3568,3571,3574],{"className":3552},[621],[587,3554],{"className":3555,"style":3501},[625],[587,3557,1846],{"className":3558},[630],[587,3560,3562],{"className":3561},[630],[587,3563,1958],{"className":3564},[1957],[587,3566,1962],{"className":3567},[630],[587,3569],{"className":3570,"style":1412},[1391],[587,3572,1271],{"className":3573},[1416],[587,3575],{"className":3576,"style":1412},[1391],[587,3578,3580,3583,3586,3592],{"className":3579},[621],[587,3581],{"className":3582,"style":3501},[625],[587,3584,1846],{"className":3585},[630],[587,3587,3589],{"className":3588},[630],[587,3590,1958],{"className":3591},[1957],[587,3593,3595],{"className":3594},[630],"048",[560,3597,3599],{"id":3598},"typische-fehler","Typische Fehler",[3601,3602,3603,3668,3846,4264],"ul",{},[3604,3605,3606,3607,3609,3610,3638,3639,3667],"li",{},"Zeilen und Spalten vertauschen. Bei der Spaltenschreibweise muss jede ",[569,3608,635],{}," die Summe ",[587,3611,3613,3626],{"className":3612},[590],[587,3614,3616],{"className":3615},[594],[596,3617,3618],{"xmlns":598},[600,3619,3620,3624],{},[603,3621,3622],{},[710,3623,712],{},[610,3625,712],{"encoding":612},[587,3627,3629],{"className":3628,"ariaHidden":617},[616],[587,3630,3632,3635],{"className":3631},[621],[587,3633],{"className":3634,"style":724},[625],[587,3636,712],{"className":3637},[630]," haben. Ist stattdessen jede Zeile ",[587,3640,3642,3655],{"className":3641},[590],[587,3643,3645],{"className":3644},[594],[596,3646,3647],{"xmlns":598},[600,3648,3649,3653],{},[603,3650,3651],{},[710,3652,712],{},[610,3654,712],{"encoding":612},[587,3656,3658],{"className":3657,"ariaHidden":617},[616],[587,3659,3661,3664],{"className":3660},[621],[587,3662],{"className":3663,"style":724},[625],[587,3665,712],{"className":3666},[630],", rechnet man mit Zeilenvektoren von links.",[3604,3669,3670,3757,3758,3845],{},[587,3671,3673,3695],{"className":3672},[590],[587,3674,3676],{"className":3675},[594],[596,3677,3678],{"xmlns":598},[600,3679,3680,3692],{},[603,3681,3682,3684,3686],{},[606,3683,608],{},[755,3685,2258],{},[749,3687,3688,3690],{"accent":617},[606,3689,753],{},[755,3691,757],{},[610,3693,3694],{"encoding":612},"A \\cdot \\vec{v}",[587,3696,3698,3716],{"className":3697,"ariaHidden":617},[616],[587,3699,3701,3704,3707,3710,3713],{"className":3700},[621],[587,3702],{"className":3703,"style":626},[625],[587,3705,608],{"className":3706},[630,631],[587,3708],{"className":3709,"style":2845},[1391],[587,3711,2258],{"className":3712},[1373],[587,3714],{"className":3715,"style":2845},[1391],[587,3717,3719,3722],{"className":3718},[621],[587,3720],{"className":3721,"style":793},[625],[587,3723,3725],{"className":3724},[630,780],[587,3726,3728],{"className":3727},[784],[587,3729,3731],{"className":3730},[788],[587,3732,3734,3742],{"className":3733,"style":793},[792],[587,3735,3736,3739],{"style":796},[587,3737],{"className":3738,"style":801},[800],[587,3740,753],{"className":3741,"style":805},[630,631],[587,3743,3744,3747],{"style":796},[587,3745],{"className":3746,"style":801},[800],[587,3748,3750],{"className":3749,"style":815},[814],[587,3751,3753],{"className":3752,"style":820},[819],[822,3754,3755],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,3756],{"d":833}," und ",[587,3759,3761,3783],{"className":3760},[590],[587,3762,3764],{"className":3763},[594],[596,3765,3766],{"xmlns":598},[600,3767,3768,3780],{},[603,3769,3770,3776,3778],{},[749,3771,3772,3774],{"accent":617},[606,3773,753],{},[755,3775,757],{},[755,3777,2258],{},[606,3779,608],{},[610,3781,3782],{"encoding":612},"\\vec{v} \\cdot A",[587,3784,3786,3836],{"className":3785,"ariaHidden":617},[616],[587,3787,3789,3792,3827,3830,3833],{"className":3788},[621],[587,3790],{"className":3791,"style":793},[625],[587,3793,3795],{"className":3794},[630,780],[587,3796,3798],{"className":3797},[784],[587,3799,3801],{"className":3800},[788],[587,3802,3804,3812],{"className":3803,"style":793},[792],[587,3805,3806,3809],{"style":796},[587,3807],{"className":3808,"style":801},[800],[587,3810,753],{"className":3811,"style":805},[630,631],[587,3813,3814,3817],{"style":796},[587,3815],{"className":3816,"style":801},[800],[587,3818,3820],{"className":3819,"style":815},[814],[587,3821,3823],{"className":3822,"style":820},[819],[822,3824,3825],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,3826],{"d":833},[587,3828],{"className":3829,"style":2845},[1391],[587,3831,2258],{"className":3832},[1373],[587,3834],{"className":3835,"style":2845},[1391],[587,3837,3839,3842],{"className":3838},[621],[587,3840],{"className":3841,"style":626},[625],[587,3843,608],{"className":3844},[630,631]," verwechseln. Die Matrixmultiplikation ist nicht kommutativ.",[3604,3847,3848,3193,3953,4104,4105,4263],{},[587,3849,3851,3872],{"className":3850},[590],[587,3852,3854],{"className":3853},[594],[596,3855,3856],{"xmlns":598},[600,3857,3858,3870],{},[603,3859,3860],{},[746,3861,3862,3868],{},[749,3863,3864,3866],{"accent":617},[606,3865,753],{},[755,3867,757],{},[606,3869,760],{},[610,3871,763],{"encoding":612},[587,3873,3875],{"className":3874,"ariaHidden":617},[616],[587,3876,3878,3881],{"className":3877},[621],[587,3879],{"className":3880,"style":773},[625],[587,3882,3884,3919],{"className":3883},[630],[587,3885,3887],{"className":3886},[630,780],[587,3888,3890],{"className":3889},[784],[587,3891,3893],{"className":3892},[788],[587,3894,3896,3904],{"className":3895,"style":793},[792],[587,3897,3898,3901],{"style":796},[587,3899],{"className":3900,"style":801},[800],[587,3902,753],{"className":3903,"style":805},[630,631],[587,3905,3906,3909],{"style":796},[587,3907],{"className":3908,"style":801},[800],[587,3910,3912],{"className":3911,"style":815},[814],[587,3913,3915],{"className":3914,"style":820},[819],[822,3916,3917],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,3918],{"d":833},[587,3920,3922],{"className":3921},[837],[587,3923,3925,3945],{"className":3924},[784,841],[587,3926,3928,3942],{"className":3927},[788],[587,3929,3931],{"className":3930,"style":848},[792],[587,3932,3933,3936],{"style":851},[587,3934],{"className":3935,"style":855},[800],[587,3937,3939],{"className":3938},[859,860,861,862],[587,3940,760],{"className":3941},[630,631,862],[587,3943,870],{"className":3944},[869],[587,3946,3948],{"className":3947},[788],[587,3949,3951],{"className":3950,"style":877},[792],[587,3952],{},[587,3954,3956,3986],{"className":3955},[590],[587,3957,3959],{"className":3958},[594],[596,3960,3961],{"xmlns":598},[600,3962,3963,3983],{},[603,3964,3965,3967,3969,3971,3973],{},[606,3966,760],{},[755,3968,2258],{},[606,3970,608],{},[755,3972,2258],{},[746,3974,3975,3981],{},[749,3976,3977,3979],{"accent":617},[606,3978,753],{},[755,3980,757],{},[710,3982,1846],{},[610,3984,3985],{"encoding":612},"n \\cdot A \\cdot \\vec{v}_0",[587,3987,3989,4008,4026],{"className":3988,"ariaHidden":617},[616],[587,3990,3992,3996,3999,4002,4005],{"className":3991},[621],[587,3993],{"className":3994,"style":3995},[625],"height:0.4445em;",[587,3997,760],{"className":3998},[630,631],[587,4000],{"className":4001,"style":2845},[1391],[587,4003,2258],{"className":4004},[1373],[587,4006],{"className":4007,"style":2845},[1391],[587,4009,4011,4014,4017,4020,4023],{"className":4010},[621],[587,4012],{"className":4013,"style":626},[625],[587,4015,608],{"className":4016},[630,631],[587,4018],{"className":4019,"style":2845},[1391],[587,4021,2258],{"className":4022},[1373],[587,4024],{"className":4025,"style":2845},[1391],[587,4027,4029,4032],{"className":4028},[621],[587,4030],{"className":4031,"style":773},[625],[587,4033,4035,4070],{"className":4034},[630],[587,4036,4038],{"className":4037},[630,780],[587,4039,4041],{"className":4040},[784],[587,4042,4044],{"className":4043},[788],[587,4045,4047,4055],{"className":4046,"style":793},[792],[587,4048,4049,4052],{"style":796},[587,4050],{"className":4051,"style":801},[800],[587,4053,753],{"className":4054,"style":805},[630,631],[587,4056,4057,4060],{"style":796},[587,4058],{"className":4059,"style":801},[800],[587,4061,4063],{"className":4062,"style":815},[814],[587,4064,4066],{"className":4065,"style":820},[819],[822,4067,4068],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,4069],{"d":833},[587,4071,4073],{"className":4072},[837],[587,4074,4076,4096],{"className":4075},[784,841],[587,4077,4079,4093],{"className":4078},[788],[587,4080,4082],{"className":4081,"style":2359},[792],[587,4083,4084,4087],{"style":851},[587,4085],{"className":4086,"style":855},[800],[587,4088,4090],{"className":4089},[859,860,861,862],[587,4091,1846],{"className":4092},[630,862],[587,4094,870],{"className":4095},[869],[587,4097,4099],{"className":4098},[788],[587,4100,4102],{"className":4101,"style":877},[792],[587,4103],{}," statt ",[587,4106,4108,4138],{"className":4107},[590],[587,4109,4111],{"className":4110},[594],[596,4112,4113],{"xmlns":598},[600,4114,4115,4135],{},[603,4116,4117,4123,4125],{},[953,4118,4119,4121],{},[606,4120,608],{},[606,4122,760],{},[755,4124,2258],{},[746,4126,4127,4133],{},[749,4128,4129,4131],{"accent":617},[606,4130,753],{},[755,4132,757],{},[710,4134,1846],{},[610,4136,4137],{"encoding":612},"A^n \\cdot \\vec{v}_0",[587,4139,4141,4185],{"className":4140,"ariaHidden":617},[616],[587,4142,4144,4147,4176,4179,4182],{"className":4143},[621],[587,4145],{"className":4146,"style":626},[625],[587,4148,4150,4153],{"className":4149},[630],[587,4151,608],{"className":4152},[630,631],[587,4154,4156],{"className":4155},[837],[587,4157,4159],{"className":4158},[784],[587,4160,4162],{"className":4161},[788],[587,4163,4165],{"className":4164,"style":989},[792],[587,4166,4167,4170],{"style":992},[587,4168],{"className":4169,"style":855},[800],[587,4171,4173],{"className":4172},[859,860,861,862],[587,4174,760],{"className":4175},[630,631,862],[587,4177],{"className":4178,"style":2845},[1391],[587,4180,2258],{"className":4181},[1373],[587,4183],{"className":4184,"style":2845},[1391],[587,4186,4188,4191],{"className":4187},[621],[587,4189],{"className":4190,"style":773},[625],[587,4192,4194,4229],{"className":4193},[630],[587,4195,4197],{"className":4196},[630,780],[587,4198,4200],{"className":4199},[784],[587,4201,4203],{"className":4202},[788],[587,4204,4206,4214],{"className":4205,"style":793},[792],[587,4207,4208,4211],{"style":796},[587,4209],{"className":4210,"style":801},[800],[587,4212,753],{"className":4213,"style":805},[630,631],[587,4215,4216,4219],{"style":796},[587,4217],{"className":4218,"style":801},[800],[587,4220,4222],{"className":4221,"style":815},[814],[587,4223,4225],{"className":4224,"style":820},[819],[822,4226,4227],{"xmlns":824,"width":825,"height":826,"style":827,"viewBox":828,"preserveAspectRatio":829},[831,4228],{"d":833},[587,4230,4232],{"className":4231},[837],[587,4233,4235,4255],{"className":4234},[784,841],[587,4236,4238,4252],{"className":4237},[788],[587,4239,4241],{"className":4240,"style":2359},[792],[587,4242,4243,4246],{"style":851},[587,4244],{"className":4245,"style":855},[800],[587,4247,4249],{"className":4248},[859,860,861,862],[587,4250,1846],{"className":4251},[630,862],[587,4253,870],{"className":4254},[869],[587,4256,4258],{"className":4257},[788],[587,4259,4261],{"className":4260,"style":877},[792],[587,4262],{}," berechnen.",[3604,4265,4266],{},"Die Markow-Eigenschaft ohne Prüfung annehmen, obwohl der nächste Zustand auch von früheren Zuständen abhängt.",{"title":4268,"searchDepth":4269,"depth":4269,"links":4270},"",2,[4271,4272,4273],{"id":562,"depth":4269,"text":563},{"id":1634,"depth":4269,"text":1635},{"id":3598,"depth":4269,"text":3599},[4275,4278,4281,4284,4287,4290,4293,4295,4297,4299,4302],{"lhs":4276,"rhs":4277},"multiply([[0.8, 0.3], [0.2, 0.7]], [0.5, 0.5])[1]","0.55",{"lhs":4279,"rhs":4280},"multiply([[0.8, 0.3], [0.2, 0.7]], [0.5, 0.5])[2]","0.45",{"lhs":4282,"rhs":4283},"multiply([[0.8, 0.3], [0.2, 0.7]], [0.55, 0.45])[1]","0.575",{"lhs":4285,"rhs":4286},"multiply([[0.8, 0.3], [0.2, 0.7]], [0.55, 0.45])[2]","0.425",{"lhs":4288,"rhs":4289},"multiply([[0.8, 0.3], [0.2, 0.7]], [[0.8, 0.3], [0.2, 0.7]])[1, 1]","0.7",{"lhs":4291,"rhs":4292},"multiply([[0.8, 0.3], [0.2, 0.7]], [[0.8, 0.3], [0.2, 0.7]])[2, 1]","0.3",{"lhs":4294,"rhs":4280},"multiply([[0.8, 0.3], [0.2, 0.7]], [[0.8, 0.3], [0.2, 0.7]])[1, 2]",{"lhs":4296,"rhs":4277},"multiply([[0.8, 0.3], [0.2, 0.7]], [[0.8, 0.3], [0.2, 0.7]])[2, 2]",{"lhs":4298,"rhs":4283},"multiply(multiply([[0.8, 0.3], [0.2, 0.7]], [[0.8, 0.3], [0.2, 0.7]]), [0.5, 0.5])[1]",{"lhs":4300,"rhs":4301},"((1-a)*x + b*y) + (a*x + (1-b)*y)","x + y",{"lhs":4303,"rhs":4304},"0.8 * 0.2 * 0.3","0.048","a_{ij} \\geq 0,\\ \\text{jede Spaltensumme von } A \\text{ ist } 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>i\u003C\u002Fmi>\u003Cmi>j\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_{ij} \\geq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9221em;vertical-align:-0.2861em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3117em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">ij\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2861em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">jede Spaltensumme von\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">ist\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","markov-chain","\\vec{v}_{n+1} = A \\cdot \\vec{v}_n, \\qquad \\vec{v}_n = A^n \\cdot \\vec{v}_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>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{v}_{n+1} = A \\cdot \\vec{v}_n, \\qquad \\vec{v}_n = A^n \\cdot \\vec{v}_0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9223em;vertical-align:-0.2083em;\">\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\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2083em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\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: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:0.1514em;\">\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>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">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>\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:0.7144em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan 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