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E)\\,\\vec{\\pi} = \\vec{0}",[574,902,904,930,994],{"className":903,"ariaHidden":595},[612],[574,905,907,911,915,918,923,927],{"className":906},[616],[574,908],{"className":909,"style":910},[620],"height:1em;vertical-align:-0.25em;",[574,912,865],{"className":913},[914],"mopen",[574,916,868],{"className":917},[625,650],[574,919],{"className":920,"style":922},[921],"mspace","margin-right:0.2222em;",[574,924,871],{"className":925},[926],"mbin",[574,928],{"className":929,"style":922},[921],[574,931,933,936,940,944,948,983,987,991],{"className":932},[616],[574,934],{"className":935,"style":910},[620],[574,937,874],{"className":938,"style":939},[625,650],"margin-right:0.0576em;",[574,941,877],{"className":942},[943],"mclose",[574,945],{"className":946,"style":947},[921],"margin-right:0.1667em;",[574,949,951],{"className":950},[625,626],[574,952,954],{"className":953},[630],[574,955,957],{"className":956},[634],[574,958,960,968],{"className":959,"style":621},[638],[574,961,962,965],{"style":641},[574,963],{"className":964,"style":646},[645],[574,966,599],{"className":967,"style":651},[625,650],[574,969,970,973],{"style":641},[574,971],{"className":972,"style":646},[645],[574,974,976],{"className":975,"style":661},[660],[574,977,979],{"className":978,"style":666},[665],[668,980,981],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,982],{"d":679},[574,984],{"className":985,"style":986},[921],"margin-right:0.2778em;",[574,988,890],{"className":989},[990],"mrel",[574,992],{"className":993,"style":986},[921],[574,995,997,1001],{"className":996},[616],[574,998],{"className":999,"style":1000},[620],"height:0.9274em;",[574,1002,1004],{"className":1003},[625,626],[574,1005,1007],{"className":1006},[630],[574,1008,1010],{"className":1009},[634],[574,1011,1013,1021],{"className":1012,"style":1000},[638],[574,1014,1015,1018],{"style":641},[574,1016],{"className":1017,"style":646},[645],[574,1019,895],{"className":1020},[625],[574,1022,1024,1027],{"style":1023},"top:-3.2134em;",[574,1025],{"className":1026,"style":646},[645],[574,1028,1030],{"className":1029,"style":661},[660],[574,1031,1033],{"className":1032,"style":666},[665],[668,1034,1035],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1036],{"d":679}," mit der Einheitsmatrix ",[574,1039,1041,1054],{"className":1040},[577],[574,1042,1044],{"className":1043},[581],[583,1045,1046],{"xmlns":585},[587,1047,1048,1052],{},[590,1049,1050],{},[597,1051,874],{},[605,1053,874],{"encoding":607},[574,1055,1057],{"className":1056,"ariaHidden":595},[612],[574,1058,1060,1064],{"className":1059},[616],[574,1061],{"className":1062,"style":1063},[620],"height:0.6833em;",[574,1065,874],{"className":1066,"style":939},[625,650]," zusammen mit der Normierung ",[574,1069,1071,1098],{"className":1070},[577],[574,1072,1074],{"className":1073},[581],[583,1075,1076],{"xmlns":585},[587,1077,1078,1095],{},[590,1079,1080,1083,1091,1093],{},[601,1081,1082],{},"∑",[1084,1085,1086,1088],"msub",{},[597,1087,599],{},[597,1089,1090],{},"i",[601,1092,890],{},[828,1094,830],{},[605,1096,1097],{"encoding":607},"\\sum \\pi_i = 1",[574,1099,1101,1178],{"className":1100,"ariaHidden":595},[612],[574,1102,1104,1107,1114,1117,1169,1172,1175],{"className":1103},[616],[574,1105],{"className":1106,"style":910},[620],[574,1108,1082],{"className":1109,"style":1113},[1110,1111,1112],"mop","op-symbol","small-op","position:relative;top:0em;",[574,1115],{"className":1116,"style":947},[921],[574,1118,1120,1123],{"className":1119},[625],[574,1121,599],{"className":1122,"style":651},[625,650],[574,1124,1127],{"className":1125},[1126],"msupsub",[574,1128,1131,1160],{"className":1129},[630,1130],"vlist-t2",[574,1132,1134,1155],{"className":1133},[634],[574,1135,1138],{"className":1136,"style":1137},[638],"height:0.3117em;",[574,1139,1141,1145],{"style":1140},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[574,1142],{"className":1143,"style":1144},[645],"height:2.7em;",[574,1146,1152],{"className":1147},[1148,1149,1150,1151],"sizing","reset-size6","size3","mtight",[574,1153,1090],{"className":1154},[625,650,1151],[574,1156,1159],{"className":1157},[1158],"vlist-s","​",[574,1161,1163],{"className":1162},[634],[574,1164,1167],{"className":1165,"style":1166},[638],"height:0.15em;",[574,1168],{},[574,1170],{"className":1171,"style":986},[921],[574,1173,890],{"className":1174},[990],[574,1176],{"className":1177,"style":986},[921],[574,1179,1181,1184],{"className":1180},[616],[574,1182],{"className":1183,"style":842},[620],[574,1185,830],{"className":1186},[625],". Eine der Gleichungen aus ",[574,1189,1191,1228],{"className":1190},[577],[574,1192,1194],{"className":1193},[581],[583,1195,1196],{"xmlns":585},[587,1197,1198,1226],{},[590,1199,1200,1202,1204,1206,1208,1210,1212,1218,1220],{},[601,1201,865],{"stretchy":864},[597,1203,868],{},[601,1205,871],{},[597,1207,874],{},[601,1209,877],{"stretchy":864},[879,1211,881],{},[593,1213,1214,1216],{"accent":595},[597,1215,599],{},[601,1217,603],{},[601,1219,890],{},[593,1221,1222,1224],{"accent":595},[828,1223,895],{},[601,1225,603],{},[605,1227,900],{"encoding":607},[574,1229,1231,1252,1311],{"className":1230,"ariaHidden":595},[612],[574,1232,1234,1237,1240,1243,1246,1249],{"className":1233},[616],[574,1235],{"className":1236,"style":910},[620],[574,1238,865],{"className":1239},[914],[574,1241,868],{"className":1242},[625,650],[574,1244],{"className":1245,"style":922},[921],[574,1247,871],{"className":1248},[926],[574,1250],{"className":1251,"style":922},[921],[574,1253,1255,1258,1261,1264,1267,1302,1305,1308],{"className":1254},[616],[574,1256],{"className":1257,"style":910},[620],[574,1259,874],{"className":1260,"style":939},[625,650],[574,1262,877],{"className":1263},[943],[574,1265],{"className":1266,"style":947},[921],[574,1268,1270],{"className":1269},[625,626],[574,1271,1273],{"className":1272},[630],[574,1274,1276],{"className":1275},[634],[574,1277,1279,1287],{"className":1278,"style":621},[638],[574,1280,1281,1284],{"style":641},[574,1282],{"className":1283,"style":646},[645],[574,1285,599],{"className":1286,"style":651},[625,650],[574,1288,1289,1292],{"style":641},[574,1290],{"className":1291,"style":646},[645],[574,1293,1295],{"className":1294,"style":661},[660],[574,1296,1298],{"className":1297,"style":666},[665],[668,1299,1300],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1301],{"d":679},[574,1303],{"className":1304,"style":986},[921],[574,1306,890],{"className":1307},[990],[574,1309],{"className":1310,"style":986},[921],[574,1312,1314,1317],{"className":1313},[616],[574,1315],{"className":1316,"style":1000},[620],[574,1318,1320],{"className":1319},[625,626],[574,1321,1323],{"className":1322},[630],[574,1324,1326],{"className":1325},[634],[574,1327,1329,1337],{"className":1328,"style":1000},[638],[574,1330,1331,1334],{"style":641},[574,1332],{"className":1333,"style":646},[645],[574,1335,895],{"className":1336},[625],[574,1338,1339,1342],{"style":1023},[574,1340],{"className":1341,"style":646},[645],[574,1343,1345],{"className":1344,"style":661},[660],[574,1346,1348],{"className":1347,"style":666},[665],[668,1349,1350],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1351],{"d":679}," ist überflüssig und wird durch die Normierung ersetzt.",[565,1354,1355],{},"Existenz, Eindeutigkeit und Konvergenz für endlich viele Zustände:",[1357,1358,1359,1363,1374],"ul",{},[1360,1361,1362],"li",{},"Eine stationäre Verteilung existiert immer.",[1360,1364,1365,1366,1369,1370,1373],{},"Sie ist ",[569,1367,1368],{},"eindeutig",", wenn die Kette ",[569,1371,1372],{},"irreduzibel"," ist (jeder Zustand ist von jedem aus erreichbar).",[1360,1375,1376,1377,1380,1381,1445,1446,1670,1671,1674,1675,1739,1740,846],{},"Ist die Kette zusätzlich ",[569,1378,1379],{},"aperiodisch"," (z.B. wenn eine Potenz ",[574,1382,1384,1404],{"className":1383},[577],[574,1385,1387],{"className":1386},[581],[583,1388,1389],{"xmlns":585},[587,1390,1391,1401],{},[590,1392,1393],{},[1394,1395,1396,1398],"msup",{},[597,1397,868],{},[597,1399,1400],{},"k",[605,1402,1403],{"encoding":607},"A^k",[574,1405,1407],{"className":1406,"ariaHidden":595},[612],[574,1408,1410,1414],{"className":1409},[616],[574,1411],{"className":1412,"style":1413},[620],"height:0.8491em;",[574,1415,1417,1420],{"className":1416},[625],[574,1418,868],{"className":1419},[625,650],[574,1421,1423],{"className":1422},[1126],[574,1424,1426],{"className":1425},[630],[574,1427,1429],{"className":1428},[634],[574,1430,1432],{"className":1431,"style":1413},[638],[574,1433,1435,1438],{"style":1434},"top:-3.063em;margin-right:0.05em;",[574,1436],{"className":1437,"style":1144},[645],[574,1439,1441],{"className":1440},[1148,1149,1150,1151],[574,1442,1400],{"className":1443,"style":1444},[625,650,1151],"margin-right:0.0315em;"," nur positive Einträge hat), dann konvergiert ",[574,1447,1449,1491],{"className":1448},[577],[574,1450,1452],{"className":1451},[581],[583,1453,1454],{"xmlns":585},[587,1455,1456,1488],{},[590,1457,1458,1465,1468,1479,1482],{},[1394,1459,1460,1462],{},[597,1461,868],{},[597,1463,1464],{},"n",[601,1466,1467],{},"⋅",[1084,1469,1470,1477],{},[593,1471,1472,1475],{"accent":595},[597,1473,1474],{},"v",[601,1476,603],{},[828,1478,895],{},[601,1480,1481],{},"→",[593,1483,1484,1486],{"accent":595},[597,1485,599],{},[601,1487,603],{},[605,1489,1490],{"encoding":607},"A^n \\cdot \\vec{v}_0 \\to \\vec{\\pi}",[574,1492,1494,1539,1629],{"className":1493,"ariaHidden":595},[612],[574,1495,1497,1500,1530,1533,1536],{"className":1496},[616],[574,1498],{"className":1499,"style":1063},[620],[574,1501,1503,1506],{"className":1502},[625],[574,1504,868],{"className":1505},[625,650],[574,1507,1509],{"className":1508},[1126],[574,1510,1512],{"className":1511},[630],[574,1513,1515],{"className":1514},[634],[574,1516,1519],{"className":1517,"style":1518},[638],"height:0.6644em;",[574,1520,1521,1524],{"style":1434},[574,1522],{"className":1523,"style":1144},[645],[574,1525,1527],{"className":1526},[1148,1149,1150,1151],[574,1528,1464],{"className":1529},[625,650,1151],[574,1531],{"className":1532,"style":922},[921],[574,1534,1467],{"className":1535},[926],[574,1537],{"className":1538,"style":922},[921],[574,1540,1542,1546,1620,1623,1626],{"className":1541},[616],[574,1543],{"className":1544,"style":1545},[620],"height:0.864em;vertical-align:-0.15em;",[574,1547,1549,1585],{"className":1548},[625],[574,1550,1552],{"className":1551},[625,626],[574,1553,1555],{"className":1554},[630],[574,1556,1558],{"className":1557},[634],[574,1559,1561,1569],{"className":1560,"style":621},[638],[574,1562,1563,1566],{"style":641},[574,1564],{"className":1565,"style":646},[645],[574,1567,1474],{"className":1568,"style":651},[625,650],[574,1570,1571,1574],{"style":641},[574,1572],{"className":1573,"style":646},[645],[574,1575,1578],{"className":1576,"style":1577},[660],"left:-0.2077em;",[574,1579,1581],{"className":1580,"style":666},[665],[668,1582,1583],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1584],{"d":679},[574,1586,1588],{"className":1587},[1126],[574,1589,1591,1612],{"className":1590},[630,1130],[574,1592,1594,1609],{"className":1593},[634],[574,1595,1598],{"className":1596,"style":1597},[638],"height:0.3011em;",[574,1599,1600,1603],{"style":1140},[574,1601],{"className":1602,"style":1144},[645],[574,1604,1606],{"className":1605},[1148,1149,1150,1151],[574,1607,895],{"className":1608},[625,1151],[574,1610,1159],{"className":1611},[1158],[574,1613,1615],{"className":1614},[634],[574,1616,1618],{"className":1617,"style":1166},[638],[574,1619],{},[574,1621],{"className":1622,"style":986},[921],[574,1624,1481],{"className":1625},[990],[574,1627],{"className":1628,"style":986},[921],[574,1630,1632,1635],{"className":1631},[616],[574,1633],{"className":1634,"style":621},[620],[574,1636,1638],{"className":1637},[625,626],[574,1639,1641],{"className":1640},[630],[574,1642,1644],{"className":1643},[634],[574,1645,1647,1655],{"className":1646,"style":621},[638],[574,1648,1649,1652],{"style":641},[574,1650],{"className":1651,"style":646},[645],[574,1653,599],{"className":1654,"style":651},[625,650],[574,1656,1657,1660],{"style":641},[574,1658],{"className":1659,"style":646},[645],[574,1661,1663],{"className":1662,"style":661},[660],[574,1664,1666],{"className":1665,"style":666},[665],[668,1667,1668],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1669],{"d":679}," für ",[569,1672,1673],{},"jeden"," Startvektor. ",[574,1676,1678,1695],{"className":1677},[577],[574,1679,1681],{"className":1680},[581],[583,1682,1683],{"xmlns":585},[587,1684,1685,1693],{},[590,1686,1687],{},[593,1688,1689,1691],{"accent":595},[597,1690,599],{},[601,1692,603],{},[605,1694,608],{"encoding":607},[574,1696,1698],{"className":1697,"ariaHidden":595},[612],[574,1699,1701,1704],{"className":1700},[616],[574,1702],{"className":1703,"style":621},[620],[574,1705,1707],{"className":1706},[625,626],[574,1708,1710],{"className":1709},[630],[574,1711,1713],{"className":1712},[634],[574,1714,1716,1724],{"className":1715,"style":621},[638],[574,1717,1718,1721],{"style":641},[574,1719],{"className":1720,"style":646},[645],[574,1722,599],{"className":1723,"style":651},[625,650],[574,1725,1726,1729],{"style":641},[574,1727],{"className":1728,"style":646},[645],[574,1730,1732],{"className":1731,"style":661},[660],[574,1733,1735],{"className":1734,"style":666},[665],[668,1736,1737],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,1738],{"d":679}," ist dann die ",[569,1741,552],{},[565,1743,1744,1745,1775,1776,1806,1807,1884],{},"Für zwei Zustände mit Wechselwahrscheinlichkeiten ",[574,1746,1748,1762],{"className":1747},[577],[574,1749,1751],{"className":1750},[581],[583,1752,1753],{"xmlns":585},[587,1754,1755,1760],{},[590,1756,1757],{},[597,1758,1759],{},"a",[605,1761,1759],{"encoding":607},[574,1763,1765],{"className":1764,"ariaHidden":595},[612],[574,1766,1768,1772],{"className":1767},[616],[574,1769],{"className":1770,"style":1771},[620],"height:0.4306em;",[574,1773,1759],{"className":1774},[625,650]," (von 1 nach 2) und ",[574,1777,1779,1793],{"className":1778},[577],[574,1780,1782],{"className":1781},[581],[583,1783,1784],{"xmlns":585},[587,1785,1786,1791],{},[590,1787,1788],{},[597,1789,1790],{},"b",[605,1792,1790],{"encoding":607},[574,1794,1796],{"className":1795,"ariaHidden":595},[612],[574,1797,1799,1803],{"className":1798},[616],[574,1800],{"className":1801,"style":1802},[620],"height:0.6944em;",[574,1804,1790],{"className":1805},[625,650]," (von 2 nach 1), ",[574,1808,1810,1834],{"className":1809},[577],[574,1811,1813],{"className":1812},[581],[583,1814,1815],{"xmlns":585},[587,1816,1817,1831],{},[590,1818,1819,1821,1824,1826,1829],{},[597,1820,1759],{},[601,1822,1823],{},"+",[597,1825,1790],{},[601,1827,1828],{},">",[828,1830,895],{},[605,1832,1833],{"encoding":607},"a + b > 0",[574,1835,1837,1856,1875],{"className":1836,"ariaHidden":595},[612],[574,1838,1840,1844,1847,1850,1853],{"className":1839},[616],[574,1841],{"className":1842,"style":1843},[620],"height:0.6667em;vertical-align:-0.0833em;",[574,1845,1759],{"className":1846},[625,650],[574,1848],{"className":1849,"style":922},[921],[574,1851,1823],{"className":1852},[926],[574,1854],{"className":1855,"style":922},[921],[574,1857,1859,1863,1866,1869,1872],{"className":1858},[616],[574,1860],{"className":1861,"style":1862},[620],"height:0.7335em;vertical-align:-0.0391em;",[574,1864,1790],{"className":1865},[625,650],[574,1867],{"className":1868,"style":986},[921],[574,1870,1828],{"className":1871},[990],[574,1873],{"className":1874,"style":986},[921],[574,1876,1878,1881],{"className":1877},[616],[574,1879],{"className":1880,"style":842},[620],[574,1882,895],{"className":1883},[625],", gilt",[574,1886,1889],{"className":1887},[1888],"katex-display",[574,1890,1892,1965],{"className":1891},[577],[574,1893,1895],{"className":1894},[581],[583,1896,1898],{"xmlns":585,"display":1897},"block",[587,1899,1900,1962],{},[590,1901,1902,1908,1910],{},[593,1903,1904,1906],{"accent":595},[597,1905,599],{},[601,1907,603],{},[601,1909,890],{},[590,1911,1912,1914,1960],{},[601,1913,865],{"fence":595},[1915,1916,1920,1942],"mtable",{"rowspacing":1917,"columnalign":1918,"columnspacing":1919},"0.16em","center","1em",[1921,1922,1923],"mtr",{},[1924,1925,1926],"mtd",{},[1927,1928,1929],"mstyle",{"scriptlevel":895,"displaystyle":864},[1930,1931,1932,1934],"mfrac",{},[597,1933,1790],{},[590,1935,1936,1938,1940],{},[597,1937,1759],{},[601,1939,1823],{},[597,1941,1790],{},[1921,1943,1944],{},[1924,1945,1946],{},[1927,1947,1948],{"scriptlevel":895,"displaystyle":864},[1930,1949,1950,1952],{},[597,1951,1759],{},[590,1953,1954,1956,1958],{},[597,1955,1759],{},[601,1957,1823],{},[597,1959,1790],{},[601,1961,877],{"fence":595},[605,1963,1964],{"encoding":607},"\\vec{\\pi} = \\begin{pmatrix} \\frac{b}{a+b} \\\\[2pt] \\frac{a}{a+b} \\end{pmatrix}",[574,1966,1968,2018],{"className":1967,"ariaHidden":595},[612],[574,1969,1971,1974,2009,2012,2015],{"className":1970},[616],[574,1972],{"className":1973,"style":621},[620],[574,1975,1977],{"className":1976},[625,626],[574,1978,1980],{"className":1979},[630],[574,1981,1983],{"className":1982},[634],[574,1984,1986,1994],{"className":1985,"style":621},[638],[574,1987,1988,1991],{"style":641},[574,1989],{"className":1990,"style":646},[645],[574,1992,599],{"className":1993,"style":651},[625,650],[574,1995,1996,1999],{"style":641},[574,1997],{"className":1998,"style":646},[645],[574,2000,2002],{"className":2001,"style":661},[660],[574,2003,2005],{"className":2004,"style":666},[665],[668,2006,2007],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2008],{"d":679},[574,2010],{"className":2011,"style":986},[921],[574,2013,890],{"className":2014},[990],[574,2016],{"className":2017,"style":986},[921],[574,2019,2021,2025],{"className":2020},[616],[574,2022],{"className":2023,"style":2024},[620],"height:3em;vertical-align:-1.25em;",[574,2026,2029,2039,2246],{"className":2027},[2028],"minner",[574,2030,2034],{"className":2031,"style":2033},[914,2032],"delimcenter","top:0em;",[574,2035,865],{"className":2036},[2037,2038],"delimsizing","size4",[574,2040,2042],{"className":2041},[625],[574,2043,2045],{"className":2044},[1915],[574,2046,2049],{"className":2047},[2048],"col-align-c",[574,2050,2052,2237],{"className":2051},[630,1130],[574,2053,2055,2234],{"className":2054},[634],[574,2056,2059,2150],{"className":2057,"style":2058},[638],"height:1.5917em;",[574,2060,2062,2065],{"style":2061},"top:-3.7116em;",[574,2063],{"className":2064,"style":646},[645],[574,2066,2068],{"className":2067},[625],[574,2069,2071,2075,2147],{"className":2070},[625],[574,2072],{"className":2073},[914,2074],"nulldelimiter",[574,2076,2078],{"className":2077},[1930],[574,2079,2081,2138],{"className":2080},[630,1130],[574,2082,2084,2135],{"className":2083},[634],[574,2085,2088,2109,2120],{"className":2086,"style":2087},[638],"height:0.8801em;",[574,2089,2091,2094],{"style":2090},"top:-2.655em;",[574,2092],{"className":2093,"style":646},[645],[574,2095,2097],{"className":2096},[1148,1149,1150,1151],[574,2098,2100,2103,2106],{"className":2099},[625,1151],[574,2101,1759],{"className":2102},[625,650,1151],[574,2104,1823],{"className":2105},[926,1151],[574,2107,1790],{"className":2108},[625,650,1151],[574,2110,2112,2115],{"style":2111},"top:-3.23em;",[574,2113],{"className":2114,"style":646},[645],[574,2116],{"className":2117,"style":2119},[2118],"frac-line","border-bottom-width:0.04em;",[574,2121,2123,2126],{"style":2122},"top:-3.394em;",[574,2124],{"className":2125,"style":646},[645],[574,2127,2129],{"className":2128},[1148,1149,1150,1151],[574,2130,2132],{"className":2131},[625,1151],[574,2133,1790],{"className":2134},[625,650,1151],[574,2136,1159],{"className":2137},[1158],[574,2139,2141],{"className":2140},[634],[574,2142,2145],{"className":2143,"style":2144},[638],"height:0.4033em;",[574,2146],{},[574,2148],{"className":2149},[943,2074],[574,2151,2153,2156],{"style":2152},"top:-2.3116em;",[574,2154],{"className":2155,"style":646},[645],[574,2157,2159],{"className":2158},[625],[574,2160,2162,2165,2231],{"className":2161},[625],[574,2163],{"className":2164},[914,2074],[574,2166,2168],{"className":2167},[1930],[574,2169,2171,2223],{"className":2170},[630,1130],[574,2172,2174,2220],{"className":2173},[634],[574,2175,2178,2198,2206],{"className":2176,"style":2177},[638],"height:0.6954em;",[574,2179,2180,2183],{"style":2090},[574,2181],{"className":2182,"style":646},[645],[574,2184,2186],{"className":2185},[1148,1149,1150,1151],[574,2187,2189,2192,2195],{"className":2188},[625,1151],[574,2190,1759],{"className":2191},[625,650,1151],[574,2193,1823],{"className":2194},[926,1151],[574,2196,1790],{"className":2197},[625,650,1151],[574,2199,2200,2203],{"style":2111},[574,2201],{"className":2202,"style":646},[645],[574,2204],{"className":2205,"style":2119},[2118],[574,2207,2208,2211],{"style":2122},[574,2209],{"className":2210,"style":646},[645],[574,2212,2214],{"className":2213},[1148,1149,1150,1151],[574,2215,2217],{"className":2216},[625,1151],[574,2218,1759],{"className":2219},[625,650,1151],[574,2221,1159],{"className":2222},[1158],[574,2224,2226],{"className":2225},[634],[574,2227,2229],{"className":2228,"style":2144},[638],[574,2230],{},[574,2232],{"className":2233},[943,2074],[574,2235,1159],{"className":2236},[1158],[574,2238,2240],{"className":2239},[634],[574,2241,2244],{"className":2242,"style":2243},[638],"height:1.0917em;",[574,2245],{},[574,2247,2249],{"className":2248,"style":2033},[943,2032],[574,2250,877],{"className":2251},[2037,2038],[565,2253,2254,2255,2468,2469,846],{},"In der Zeilenschreibweise vieler Lehrbücher lautet die Bedingung ",[574,2256,2258,2304],{"className":2257},[577],[574,2259,2261],{"className":2260},[581],[583,2262,2263],{"xmlns":585},[587,2264,2265,2301],{},[590,2266,2267,2282,2285,2287],{},[1394,2268,2269,2275],{},[593,2270,2271,2273],{"accent":595},[597,2272,599],{},[601,2274,603],{},[590,2276,2277,2279],{},[879,2278,881],{},[597,2280,2281],{},"T",[597,2283,2284],{},"P",[601,2286,890],{},[1394,2288,2289,2295],{},[593,2290,2291,2293],{"accent":595},[597,2292,599],{},[601,2294,603],{},[590,2296,2297,2299],{},[879,2298,881],{},[597,2300,2281],{},[605,2302,2303],{"encoding":607},"\\vec{\\pi}^{\\,T} P = \\vec{\\pi}^{\\,T}",[574,2305,2307,2395],{"className":2306,"ariaHidden":595},[612],[574,2308,2310,2314,2383,2386,2389,2392],{"className":2309},[616],[574,2311],{"className":2312,"style":2313},[620],"height:0.8413em;",[574,2315,2317,2352],{"className":2316},[625],[574,2318,2320],{"className":2319},[625,626],[574,2321,2323],{"className":2322},[630],[574,2324,2326],{"className":2325},[634],[574,2327,2329,2337],{"className":2328,"style":621},[638],[574,2330,2331,2334],{"style":641},[574,2332],{"className":2333,"style":646},[645],[574,2335,599],{"className":2336,"style":651},[625,650],[574,2338,2339,2342],{"style":641},[574,2340],{"className":2341,"style":646},[645],[574,2343,2345],{"className":2344,"style":661},[660],[574,2346,2348],{"className":2347,"style":666},[665],[668,2349,2350],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2351],{"d":679},[574,2353,2355],{"className":2354},[1126],[574,2356,2358],{"className":2357},[630],[574,2359,2361],{"className":2360},[634],[574,2362,2364],{"className":2363,"style":2313},[638],[574,2365,2366,2369],{"style":1434},[574,2367],{"className":2368,"style":1144},[645],[574,2370,2372],{"className":2371},[1148,1149,1150,1151],[574,2373,2375,2379],{"className":2374},[625,1151],[574,2376],{"className":2377,"style":2378},[921,1151],"margin-right:0.1952em;",[574,2380,2281],{"className":2381,"style":2382},[625,650,1151],"margin-right:0.1389em;",[574,2384,2284],{"className":2385,"style":2382},[625,650],[574,2387],{"className":2388,"style":986},[921],[574,2390,890],{"className":2391},[990],[574,2393],{"className":2394,"style":986},[921],[574,2396,2398,2401],{"className":2397},[616],[574,2399],{"className":2400,"style":2313},[620],[574,2402,2404,2439],{"className":2403},[625],[574,2405,2407],{"className":2406},[625,626],[574,2408,2410],{"className":2409},[630],[574,2411,2413],{"className":2412},[634],[574,2414,2416,2424],{"className":2415,"style":621},[638],[574,2417,2418,2421],{"style":641},[574,2419],{"className":2420,"style":646},[645],[574,2422,599],{"className":2423,"style":651},[625,650],[574,2425,2426,2429],{"style":641},[574,2427],{"className":2428,"style":646},[645],[574,2430,2432],{"className":2431,"style":661},[660],[574,2433,2435],{"className":2434,"style":666},[665],[668,2436,2437],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2438],{"d":679},[574,2440,2442],{"className":2441},[1126],[574,2443,2445],{"className":2444},[630],[574,2446,2448],{"className":2447},[634],[574,2449,2451],{"className":2450,"style":2313},[638],[574,2452,2453,2456],{"style":1434},[574,2454],{"className":2455,"style":1144},[645],[574,2457,2459],{"className":2458},[1148,1149,1150,1151],[574,2460,2462,2465],{"className":2461},[625,1151],[574,2463],{"className":2464,"style":2378},[921,1151],[574,2466,2281],{"className":2467,"style":2382},[625,650,1151]," mit ",[574,2470,2472,2494],{"className":2471},[577],[574,2473,2475],{"className":2474},[581],[583,2476,2477],{"xmlns":585},[587,2478,2479,2491],{},[590,2480,2481,2483,2485],{},[597,2482,2284],{},[601,2484,890],{},[1394,2486,2487,2489],{},[597,2488,868],{},[597,2490,2281],{},[605,2492,2493],{"encoding":607},"P = A^T",[574,2495,2497,2515],{"className":2496,"ariaHidden":595},[612],[574,2498,2500,2503,2506,2509,2512],{"className":2499},[616],[574,2501],{"className":2502,"style":1063},[620],[574,2504,2284],{"className":2505,"style":2382},[625,650],[574,2507],{"className":2508,"style":986},[921],[574,2510,890],{"className":2511},[990],[574,2513],{"className":2514,"style":986},[921],[574,2516,2518,2521],{"className":2517},[616],[574,2519],{"className":2520,"style":2313},[620],[574,2522,2524,2527],{"className":2523},[625],[574,2525,868],{"className":2526},[625,650],[574,2528,2530],{"className":2529},[1126],[574,2531,2533],{"className":2532},[630],[574,2534,2536],{"className":2535},[634],[574,2537,2539],{"className":2538,"style":2313},[638],[574,2540,2541,2544],{"style":1434},[574,2542],{"className":2543,"style":1144},[645],[574,2545,2547],{"className":2546},[1148,1149,1150,1151],[574,2548,2281],{"className":2549,"style":2382},[625,650,1151],[560,2551,2553],{"id":2552},"beispiele","Beispiele",[565,2555,2556,2557,2810,2811,2939],{},"Für die Anbieterwechsel mit ",[574,2558,2560,2617],{"className":2559},[577],[574,2561,2563],{"className":2562},[581],[583,2564,2565],{"xmlns":585},[587,2566,2567,2614],{},[590,2568,2569,2571,2573],{},[597,2570,868],{},[601,2572,890],{},[590,2574,2575,2577,2612],{},[601,2576,865],{"fence":595},[1915,2578,2580,2596],{"rowspacing":1917,"columnalign":2579,"columnspacing":1919},"center center",[1921,2581,2582,2589],{},[1924,2583,2584],{},[1927,2585,2586],{"scriptlevel":895,"displaystyle":864},[828,2587,2588],{},"0,8",[1924,2590,2591],{},[1927,2592,2593],{"scriptlevel":895,"displaystyle":864},[828,2594,2595],{},"0,3",[1921,2597,2598,2605],{},[1924,2599,2600],{},[1927,2601,2602],{"scriptlevel":895,"displaystyle":864},[828,2603,2604],{},"0,2",[1924,2606,2607],{},[1927,2608,2609],{"scriptlevel":895,"displaystyle":864},[828,2610,2611],{},"0,7",[601,2613,877],{"fence":595},[605,2615,2616],{"encoding":607},"A = \\begin{pmatrix} 0{,}8 & 0{,}3 \\\\ 0{,}2 & 0{,}7 \\end{pmatrix}",[574,2618,2620,2638],{"className":2619,"ariaHidden":595},[612],[574,2621,2623,2626,2629,2632,2635],{"className":2622},[616],[574,2624],{"className":2625,"style":1063},[620],[574,2627,868],{"className":2628},[625,650],[574,2630],{"className":2631,"style":986},[921],[574,2633,890],{"className":2634},[990],[574,2636],{"className":2637,"style":986},[921],[574,2639,2641,2645],{"className":2640},[616],[574,2642],{"className":2643,"style":2644},[620],"height:2.4em;vertical-align:-0.95em;",[574,2646,2648,2654,2804],{"className":2647},[2028],[574,2649,2651],{"className":2650,"style":2033},[914,2032],[574,2652,865],{"className":2653},[2037,1150],[574,2655,2657],{"className":2656},[625],[574,2658,2660,2731,2736,2739],{"className":2659},[1915],[574,2661,2663],{"className":2662},[2048],[574,2664,2666,2722],{"className":2665},[630,1130],[574,2667,2669,2719],{"className":2668},[634],[574,2670,2673,2697],{"className":2671,"style":2672},[638],"height:1.45em;",[574,2674,2676,2679],{"style":2675},"top:-3.61em;",[574,2677],{"className":2678,"style":646},[645],[574,2680,2682,2685,2693],{"className":2681},[625],[574,2683,895],{"className":2684},[625],[574,2686,2688],{"className":2687},[625],[574,2689,2692],{"className":2690},[2691],"mpunct",",",[574,2694,2696],{"className":2695},[625],"8",[574,2698,2700,2703],{"style":2699},"top:-2.41em;",[574,2701],{"className":2702,"style":646},[645],[574,2704,2706,2709,2715],{"className":2705},[625],[574,2707,895],{"className":2708},[625],[574,2710,2712],{"className":2711},[625],[574,2713,2692],{"className":2714},[2691],[574,2716,2718],{"className":2717},[625],"2",[574,2720,1159],{"className":2721},[1158],[574,2723,2725],{"className":2724},[634],[574,2726,2729],{"className":2727,"style":2728},[638],"height:0.95em;",[574,2730],{},[574,2732],{"className":2733,"style":2735},[2734],"arraycolsep","width:0.5em;",[574,2737],{"className":2738,"style":2735},[2734],[574,2740,2742],{"className":2741},[2048],[574,2743,2745,2796],{"className":2744},[630,1130],[574,2746,2748,2793],{"className":2747},[634],[574,2749,2751,2772],{"className":2750,"style":2672},[638],[574,2752,2753,2756],{"style":2675},[574,2754],{"className":2755,"style":646},[645],[574,2757,2759,2762,2768],{"className":2758},[625],[574,2760,895],{"className":2761},[625],[574,2763,2765],{"className":2764},[625],[574,2766,2692],{"className":2767},[2691],[574,2769,2771],{"className":2770},[625],"3",[574,2773,2774,2777],{"style":2699},[574,2775],{"className":2776,"style":646},[645],[574,2778,2780,2783,2789],{"className":2779},[625],[574,2781,895],{"className":2782},[625],[574,2784,2786],{"className":2785},[625],[574,2787,2692],{"className":2788},[2691],[574,2790,2792],{"className":2791},[625],"7",[574,2794,1159],{"className":2795},[1158],[574,2797,2799],{"className":2798},[634],[574,2800,2802],{"className":2801,"style":2728},[638],[574,2803],{},[574,2805,2807],{"className":2806,"style":2033},[943,2032],[574,2808,877],{"className":2809},[2037,1150]," liefert die erste Zeile von ",[574,2812,2814,2842],{"className":2813},[577],[574,2815,2817],{"className":2816},[581],[583,2818,2819],{"xmlns":585},[587,2820,2821,2839],{},[590,2822,2823,2825,2831,2833],{},[597,2824,868],{},[593,2826,2827,2829],{"accent":595},[597,2828,599],{},[601,2830,603],{},[601,2832,890],{},[593,2834,2835,2837],{"accent":595},[597,2836,599],{},[601,2838,603],{},[605,2840,2841],{"encoding":607},"A\\vec{\\pi} = \\vec{\\pi}",[574,2843,2845,2898],{"className":2844,"ariaHidden":595},[612],[574,2846,2848,2851,2854,2889,2892,2895],{"className":2847},[616],[574,2849],{"className":2850,"style":621},[620],[574,2852,868],{"className":2853},[625,650],[574,2855,2857],{"className":2856},[625,626],[574,2858,2860],{"className":2859},[630],[574,2861,2863],{"className":2862},[634],[574,2864,2866,2874],{"className":2865,"style":621},[638],[574,2867,2868,2871],{"style":641},[574,2869],{"className":2870,"style":646},[645],[574,2872,599],{"className":2873,"style":651},[625,650],[574,2875,2876,2879],{"style":641},[574,2877],{"className":2878,"style":646},[645],[574,2880,2882],{"className":2881,"style":661},[660],[574,2883,2885],{"className":2884,"style":666},[665],[668,2886,2887],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2888],{"d":679},[574,2890],{"className":2891,"style":986},[921],[574,2893,890],{"className":2894},[990],[574,2896],{"className":2897,"style":986},[921],[574,2899,2901,2904],{"className":2900},[616],[574,2902],{"className":2903,"style":621},[620],[574,2905,2907],{"className":2906},[625,626],[574,2908,2910],{"className":2909},[630],[574,2911,2913],{"className":2912},[634],[574,2914,2916,2924],{"className":2915,"style":621},[638],[574,2917,2918,2921],{"style":641},[574,2919],{"className":2920,"style":646},[645],[574,2922,599],{"className":2923,"style":651},[625,650],[574,2925,2926,2929],{"style":641},[574,2927],{"className":2928,"style":646},[645],[574,2930,2932],{"className":2931,"style":661},[660],[574,2933,2935],{"className":2934,"style":666},[665],[668,2936,2937],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,2938],{"d":679},":",[574,2941,2943],{"className":2942},[1888],[574,2944,2946,3017],{"className":2945},[577],[574,2947,2949],{"className":2948},[581],[583,2950,2951],{"xmlns":585,"display":1897},[587,2952,2953,3014],{},[590,2954,2955,2957,2959,2965,2967,2969,2971,2977,2979,2985,2987,2990,2992,2994,2996,3002,3004,3006,3008],{},[828,2956,2588],{},[879,2958,881],{},[1084,2960,2961,2963],{},[597,2962,599],{},[828,2964,830],{},[601,2966,1823],{},[828,2968,2595],{},[879,2970,881],{},[1084,2972,2973,2975],{},[597,2974,599],{},[828,2976,2718],{},[601,2978,890],{},[1084,2980,2981,2983],{},[597,2982,599],{},[828,2984,830],{},[921,2986],{"width":1919},[601,2988,2989],{},"⇒",[921,2991],{"width":1919},[828,2993,2595],{},[879,2995,881],{},[1084,2997,2998,3000],{},[597,2999,599],{},[828,3001,2718],{},[601,3003,890],{},[828,3005,2604],{},[879,3007,881],{},[1084,3009,3010,3012],{},[597,3011,599],{},[828,3013,830],{},[605,3015,3016],{"encoding":607},"0{,}8\\,\\pi_1 + 0{,}3\\,\\pi_2 = \\pi_1 \\quad \\Rightarrow \\quad 0{,}3\\,\\pi_2 = 0{,}2\\,\\pi_1",[574,3018,3020,3091,3161,3224,3294],{"className":3019,"ariaHidden":595},[612],[574,3021,3023,3027,3030,3036,3039,3042,3082,3085,3088],{"className":3022},[616],[574,3024],{"className":3025,"style":3026},[620],"height:0.8389em;vertical-align:-0.1944em;",[574,3028,895],{"className":3029},[625],[574,3031,3033],{"className":3032},[625],[574,3034,2692],{"className":3035},[2691],[574,3037,2696],{"className":3038},[625],[574,3040],{"className":3041,"style":947},[921],[574,3043,3045,3048],{"className":3044},[625],[574,3046,599],{"className":3047,"style":651},[625,650],[574,3049,3051],{"className":3050},[1126],[574,3052,3054,3074],{"className":3053},[630,1130],[574,3055,3057,3071],{"className":3056},[634],[574,3058,3060],{"className":3059,"style":1597},[638],[574,3061,3062,3065],{"style":1140},[574,3063],{"className":3064,"style":1144},[645],[574,3066,3068],{"className":3067},[1148,1149,1150,1151],[574,3069,830],{"className":3070},[625,1151],[574,3072,1159],{"className":3073},[1158],[574,3075,3077],{"className":3076},[634],[574,3078,3080],{"className":3079,"style":1166},[638],[574,3081],{},[574,3083],{"className":3084,"style":922},[921],[574,3086,1823],{"className":3087},[926],[574,3089],{"className":3090,"style":922},[921],[574,3092,3094,3097,3100,3106,3109,3112,3152,3155,3158],{"className":3093},[616],[574,3095],{"className":3096,"style":3026},[620],[574,3098,895],{"className":3099},[625],[574,3101,3103],{"className":3102},[625],[574,3104,2692],{"className":3105},[2691],[574,3107,2771],{"className":3108},[625],[574,3110],{"className":3111,"style":947},[921],[574,3113,3115,3118],{"className":3114},[625],[574,3116,599],{"className":3117,"style":651},[625,650],[574,3119,3121],{"className":3120},[1126],[574,3122,3124,3144],{"className":3123},[630,1130],[574,3125,3127,3141],{"className":3126},[634],[574,3128,3130],{"className":3129,"style":1597},[638],[574,3131,3132,3135],{"style":1140},[574,3133],{"className":3134,"style":1144},[645],[574,3136,3138],{"className":3137},[1148,1149,1150,1151],[574,3139,2718],{"className":3140},[625,1151],[574,3142,1159],{"className":3143},[1158],[574,3145,3147],{"className":3146},[634],[574,3148,3150],{"className":3149,"style":1166},[638],[574,3151],{},[574,3153],{"className":3154,"style":986},[921],[574,3156,890],{"className":3157},[990],[574,3159],{"className":3160,"style":986},[921],[574,3162,3164,3168,3208,3212,3215,3218,3221],{"className":3163},[616],[574,3165],{"className":3166,"style":3167},[620],"height:0.5806em;vertical-align:-0.15em;",[574,3169,3171,3174],{"className":3170},[625],[574,3172,599],{"className":3173,"style":651},[625,650],[574,3175,3177],{"className":3176},[1126],[574,3178,3180,3200],{"className":3179},[630,1130],[574,3181,3183,3197],{"className":3182},[634],[574,3184,3186],{"className":3185,"style":1597},[638],[574,3187,3188,3191],{"style":1140},[574,3189],{"className":3190,"style":1144},[645],[574,3192,3194],{"className":3193},[1148,1149,1150,1151],[574,3195,830],{"className":3196},[625,1151],[574,3198,1159],{"className":3199},[1158],[574,3201,3203],{"className":3202},[634],[574,3204,3206],{"className":3205,"style":1166},[638],[574,3207],{},[574,3209],{"className":3210,"style":3211},[921],"margin-right:1em;",[574,3213],{"className":3214,"style":986},[921],[574,3216,2989],{"className":3217},[990],[574,3219],{"className":3220,"style":3211},[921],[574,3222],{"className":3223,"style":986},[921],[574,3225,3227,3230,3233,3239,3242,3245,3285,3288,3291],{"className":3226},[616],[574,3228],{"className":3229,"style":3026},[620],[574,3231,895],{"className":3232},[625],[574,3234,3236],{"className":3235},[625],[574,3237,2692],{"className":3238},[2691],[574,3240,2771],{"className":3241},[625],[574,3243],{"className":3244,"style":947},[921],[574,3246,3248,3251],{"className":3247},[625],[574,3249,599],{"className":3250,"style":651},[625,650],[574,3252,3254],{"className":3253},[1126],[574,3255,3257,3277],{"className":3256},[630,1130],[574,3258,3260,3274],{"className":3259},[634],[574,3261,3263],{"className":3262,"style":1597},[638],[574,3264,3265,3268],{"style":1140},[574,3266],{"className":3267,"style":1144},[645],[574,3269,3271],{"className":3270},[1148,1149,1150,1151],[574,3272,2718],{"className":3273},[625,1151],[574,3275,1159],{"className":3276},[1158],[574,3278,3280],{"className":3279},[634],[574,3281,3283],{"className":3282,"style":1166},[638],[574,3284],{},[574,3286],{"className":3287,"style":986},[921],[574,3289,890],{"className":3290},[990],[574,3292],{"className":3293,"style":986},[921],[574,3295,3297,3300,3303,3309,3312,3315],{"className":3296},[616],[574,3298],{"className":3299,"style":3026},[620],[574,3301,895],{"className":3302},[625],[574,3304,3306],{"className":3305},[625],[574,3307,2692],{"className":3308},[2691],[574,3310,2718],{"className":3311},[625],[574,3313],{"className":3314,"style":947},[921],[574,3316,3318,3321],{"className":3317},[625],[574,3319,599],{"className":3320,"style":651},[625,650],[574,3322,3324],{"className":3323},[1126],[574,3325,3327,3347],{"className":3326},[630,1130],[574,3328,3330,3344],{"className":3329},[634],[574,3331,3333],{"className":3332,"style":1597},[638],[574,3334,3335,3338],{"style":1140},[574,3336],{"className":3337,"style":1144},[645],[574,3339,3341],{"className":3340},[1148,1149,1150,1151],[574,3342,830],{"className":3343},[625,1151],[574,3345,1159],{"className":3346},[1158],[574,3348,3350],{"className":3349},[634],[574,3351,3353],{"className":3352,"style":1166},[638],[574,3354],{},[565,3356,3357,3358,3514,3515,3618,3619,3722,3723,3895],{},"Mit ",[574,3359,3361,3391],{"className":3360},[577],[574,3362,3364],{"className":3363},[581],[583,3365,3366],{"xmlns":585},[587,3367,3368,3388],{},[590,3369,3370,3376,3378,3384,3386],{},[1084,3371,3372,3374],{},[597,3373,599],{},[828,3375,830],{},[601,3377,1823],{},[1084,3379,3380,3382],{},[597,3381,599],{},[828,3383,2718],{},[601,3385,890],{},[828,3387,830],{},[605,3389,3390],{"encoding":607},"\\pi_1 + \\pi_2 = 1",[574,3392,3394,3450,3505],{"className":3393,"ariaHidden":595},[612],[574,3395,3397,3401,3441,3444,3447],{"className":3396},[616],[574,3398],{"className":3399,"style":3400},[620],"height:0.7333em;vertical-align:-0.15em;",[574,3402,3404,3407],{"className":3403},[625],[574,3405,599],{"className":3406,"style":651},[625,650],[574,3408,3410],{"className":3409},[1126],[574,3411,3413,3433],{"className":3412},[630,1130],[574,3414,3416,3430],{"className":3415},[634],[574,3417,3419],{"className":3418,"style":1597},[638],[574,3420,3421,3424],{"style":1140},[574,3422],{"className":3423,"style":1144},[645],[574,3425,3427],{"className":3426},[1148,1149,1150,1151],[574,3428,830],{"className":3429},[625,1151],[574,3431,1159],{"className":3432},[1158],[574,3434,3436],{"className":3435},[634],[574,3437,3439],{"className":3438,"style":1166},[638],[574,3440],{},[574,3442],{"className":3443,"style":922},[921],[574,3445,1823],{"className":3446},[926],[574,3448],{"className":3449,"style":922},[921],[574,3451,3453,3456,3496,3499,3502],{"className":3452},[616],[574,3454],{"className":3455,"style":3167},[620],[574,3457,3459,3462],{"className":3458},[625],[574,3460,599],{"className":3461,"style":651},[625,650],[574,3463,3465],{"className":3464},[1126],[574,3466,3468,3488],{"className":3467},[630,1130],[574,3469,3471,3485],{"className":3470},[634],[574,3472,3474],{"className":3473,"style":1597},[638],[574,3475,3476,3479],{"style":1140},[574,3477],{"className":3478,"style":1144},[645],[574,3480,3482],{"className":3481},[1148,1149,1150,1151],[574,3483,2718],{"className":3484},[625,1151],[574,3486,1159],{"className":3487},[1158],[574,3489,3491],{"className":3490},[634],[574,3492,3494],{"className":3493,"style":1166},[638],[574,3495],{},[574,3497],{"className":3498,"style":986},[921],[574,3500,890],{"className":3501},[990],[574,3503],{"className":3504,"style":986},[921],[574,3506,3508,3511],{"className":3507},[616],[574,3509],{"className":3510,"style":842},[620],[574,3512,830],{"className":3513},[625]," folgt ",[574,3516,3518,3541],{"className":3517},[577],[574,3519,3521],{"className":3520},[581],[583,3522,3523],{"xmlns":585},[587,3524,3525,3538],{},[590,3526,3527,3533,3535],{},[1084,3528,3529,3531],{},[597,3530,599],{},[828,3532,830],{},[601,3534,890],{},[828,3536,3537],{},"0,6",[605,3539,3540],{"encoding":607},"\\pi_1 = 0{,}6",[574,3542,3544,3599],{"className":3543,"ariaHidden":595},[612],[574,3545,3547,3550,3590,3593,3596],{"className":3546},[616],[574,3548],{"className":3549,"style":3167},[620],[574,3551,3553,3556],{"className":3552},[625],[574,3554,599],{"className":3555,"style":651},[625,650],[574,3557,3559],{"className":3558},[1126],[574,3560,3562,3582],{"className":3561},[630,1130],[574,3563,3565,3579],{"className":3564},[634],[574,3566,3568],{"className":3567,"style":1597},[638],[574,3569,3570,3573],{"style":1140},[574,3571],{"className":3572,"style":1144},[645],[574,3574,3576],{"className":3575},[1148,1149,1150,1151],[574,3577,830],{"className":3578},[625,1151],[574,3580,1159],{"className":3581},[1158],[574,3583,3585],{"className":3584},[634],[574,3586,3588],{"className":3587,"style":1166},[638],[574,3589],{},[574,3591],{"className":3592,"style":986},[921],[574,3594,890],{"className":3595},[990],[574,3597],{"className":3598,"style":986},[921],[574,3600,3602,3605,3608,3614],{"className":3601},[616],[574,3603],{"className":3604,"style":3026},[620],[574,3606,895],{"className":3607},[625],[574,3609,3611],{"className":3610},[625],[574,3612,2692],{"className":3613},[2691],[574,3615,3617],{"className":3616},[625],"6"," und ",[574,3620,3622,3645],{"className":3621},[577],[574,3623,3625],{"className":3624},[581],[583,3626,3627],{"xmlns":585},[587,3628,3629,3642],{},[590,3630,3631,3637,3639],{},[1084,3632,3633,3635],{},[597,3634,599],{},[828,3636,2718],{},[601,3638,890],{},[828,3640,3641],{},"0,4",[605,3643,3644],{"encoding":607},"\\pi_2 = 0{,}4",[574,3646,3648,3703],{"className":3647,"ariaHidden":595},[612],[574,3649,3651,3654,3694,3697,3700],{"className":3650},[616],[574,3652],{"className":3653,"style":3167},[620],[574,3655,3657,3660],{"className":3656},[625],[574,3658,599],{"className":3659,"style":651},[625,650],[574,3661,3663],{"className":3662},[1126],[574,3664,3666,3686],{"className":3665},[630,1130],[574,3667,3669,3683],{"className":3668},[634],[574,3670,3672],{"className":3671,"style":1597},[638],[574,3673,3674,3677],{"style":1140},[574,3675],{"className":3676,"style":1144},[645],[574,3678,3680],{"className":3679},[1148,1149,1150,1151],[574,3681,2718],{"className":3682},[625,1151],[574,3684,1159],{"className":3685},[1158],[574,3687,3689],{"className":3688},[634],[574,3690,3692],{"className":3691,"style":1166},[638],[574,3693],{},[574,3695],{"className":3696,"style":986},[921],[574,3698,890],{"className":3699},[990],[574,3701],{"className":3702,"style":986},[921],[574,3704,3706,3709,3712,3718],{"className":3705},[616],[574,3707],{"className":3708,"style":3026},[620],[574,3710,895],{"className":3711},[625],[574,3713,3715],{"className":3714},[625],[574,3716,2692],{"className":3717},[2691],[574,3719,3721],{"className":3720},[625],"4",". Die Formel für zwei Zustände bestätigt das: ",[574,3724,3726,3754],{"className":3725},[577],[574,3727,3729],{"className":3728},[581],[583,3730,3731],{"xmlns":585},[587,3732,3733,3751],{},[590,3734,3735,3747,3749],{},[1930,3736,3737,3739],{},[828,3738,2595],{},[590,3740,3741,3743,3745],{},[828,3742,2604],{},[601,3744,1823],{},[828,3746,2595],{},[601,3748,890],{},[828,3750,3537],{},[605,3752,3753],{"encoding":607},"\\frac{0{,}3}{0{,}2 + 0{,}3} = 0{,}6",[574,3755,3757,3877],{"className":3756,"ariaHidden":595},[612],[574,3758,3760,3764,3868,3871,3874],{"className":3759},[616],[574,3761],{"className":3762,"style":3763},[620],"height:1.3783em;vertical-align:-0.4811em;",[574,3765,3767,3770,3865],{"className":3766},[625],[574,3768],{"className":3769},[914,2074],[574,3771,3773],{"className":3772},[1930],[574,3774,3776,3856],{"className":3775},[630,1130],[574,3777,3779,3853],{"className":3778},[634],[574,3780,3783,3821,3829],{"className":3781,"style":3782},[638],"height:0.8972em;",[574,3784,3785,3788],{"style":2090},[574,3786],{"className":3787,"style":646},[645],[574,3789,3791],{"className":3790},[1148,1149,1150,1151],[574,3792,3794,3797,3803,3806,3809,3812,3818],{"className":3793},[625,1151],[574,3795,895],{"className":3796},[625,1151],[574,3798,3800],{"className":3799},[625,1151],[574,3801,2692],{"className":3802},[2691,1151],[574,3804,2718],{"className":3805},[625,1151],[574,3807,1823],{"className":3808},[926,1151],[574,3810,895],{"className":3811},[625,1151],[574,3813,3815],{"className":3814},[625,1151],[574,3816,2692],{"className":3817},[2691,1151],[574,3819,2771],{"className":3820},[625,1151],[574,3822,3823,3826],{"style":2111},[574,3824],{"className":3825,"style":646},[645],[574,3827],{"className":3828,"style":2119},[2118],[574,3830,3832,3835],{"style":3831},"top:-3.4461em;",[574,3833],{"className":3834,"style":646},[645],[574,3836,3838],{"className":3837},[1148,1149,1150,1151],[574,3839,3841,3844,3850],{"className":3840},[625,1151],[574,3842,895],{"className":3843},[625,1151],[574,3845,3847],{"className":3846},[625,1151],[574,3848,2692],{"className":3849},[2691,1151],[574,3851,2771],{"className":3852},[625,1151],[574,3854,1159],{"className":3855},[1158],[574,3857,3859],{"className":3858},[634],[574,3860,3863],{"className":3861,"style":3862},[638],"height:0.4811em;",[574,3864],{},[574,3866],{"className":3867},[943,2074],[574,3869],{"className":3870,"style":986},[921],[574,3872,890],{"className":3873},[990],[574,3875],{"className":3876,"style":986},[921],[574,3878,3880,3883,3886,3892],{"className":3879},[616],[574,3881],{"className":3882,"style":3026},[620],[574,3884,895],{"className":3885},[625],[574,3887,3889],{"className":3888},[625],[574,3890,2692],{"className":3891},[2691],[574,3893,3617],{"className":3894},[625],". Probe:",[574,3897,3899],{"className":3898},[1888],[574,3900,3902,3992],{"className":3901},[577],[574,3903,3905],{"className":3904},[581],[583,3906,3907],{"xmlns":585,"display":1897},[587,3908,3909,3989],{},[590,3910,3911,3963,3965],{},[590,3912,3913,3915,3961],{},[601,3914,865],{"fence":595},[1915,3916,3917,3939],{"rowspacing":1917,"columnalign":1918,"columnspacing":1919},[1921,3918,3919],{},[1924,3920,3921],{},[1927,3922,3923],{"scriptlevel":895,"displaystyle":864},[590,3924,3925,3927,3929,3931,3933,3935,3937],{},[828,3926,2588],{},[601,3928,1467],{},[828,3930,3537],{},[601,3932,1823],{},[828,3934,2595],{},[601,3936,1467],{},[828,3938,3641],{},[1921,3940,3941],{},[1924,3942,3943],{},[1927,3944,3945],{"scriptlevel":895,"displaystyle":864},[590,3946,3947,3949,3951,3953,3955,3957,3959],{},[828,3948,2604],{},[601,3950,1467],{},[828,3952,3537],{},[601,3954,1823],{},[828,3956,2611],{},[601,3958,1467],{},[828,3960,3641],{},[601,3962,877],{"fence":595},[601,3964,890],{},[590,3966,3967,3969,3987],{},[601,3968,865],{"fence":595},[1915,3970,3971,3979],{"rowspacing":1917,"columnalign":1918,"columnspacing":1919},[1921,3972,3973],{},[1924,3974,3975],{},[1927,3976,3977],{"scriptlevel":895,"displaystyle":864},[828,3978,3537],{},[1921,3980,3981],{},[1924,3982,3983],{},[1927,3984,3985],{"scriptlevel":895,"displaystyle":864},[828,3986,3641],{},[601,3988,877],{"fence":595},[605,3990,3991],{"encoding":607},"\\begin{pmatrix} 0{,}8 \\cdot 0{,}6 + 0{,}3 \\cdot 0{,}4 \\\\ 0{,}2 \\cdot 0{,}6 + 0{,}7 \\cdot 0{,}4 \\end{pmatrix} = \\begin{pmatrix} 0{,}6 \\\\ 0{,}4 \\end{pmatrix}",[574,3993,3995,4220],{"className":3994,"ariaHidden":595},[612],[574,3996,3998,4001,4211,4214,4217],{"className":3997},[616],[574,3999],{"className":4000,"style":2644},[620],[574,4002,4004,4010,4205],{"className":4003},[2028],[574,4005,4007],{"className":4006,"style":2033},[914,2032],[574,4008,865],{"className":4009},[2037,1150],[574,4011,4013],{"className":4012},[625],[574,4014,4016],{"className":4015},[1915],[574,4017,4019],{"className":4018},[2048],[574,4020,4022,4197],{"className":4021},[630,1130],[574,4023,4025,4194],{"className":4024},[634],[574,4026,4028,4111],{"className":4027,"style":2672},[638],[574,4029,4030,4033],{"style":2675},[574,4031],{"className":4032,"style":646},[645],[574,4034,4036,4039,4045,4048,4051,4054,4057,4060,4066,4069,4072,4075,4078,4081,4087,4090,4093,4096,4099,4102,4108],{"className":4035},[625],[574,4037,895],{"className":4038},[625],[574,4040,4042],{"className":4041},[625],[574,4043,2692],{"className":4044},[2691],[574,4046,2696],{"className":4047},[625],[574,4049],{"className":4050,"style":922},[921],[574,4052,1467],{"className":4053},[926],[574,4055],{"className":4056,"style":922},[921],[574,4058,895],{"className":4059},[625],[574,4061,4063],{"className":4062},[625],[574,4064,2692],{"className":4065},[2691],[574,4067,3617],{"className":4068},[625],[574,4070],{"className":4071,"style":922},[921],[574,4073,1823],{"className":4074},[926],[574,4076],{"className":4077,"style":922},[921],[574,4079,895],{"className":4080},[625],[574,4082,4084],{"className":4083},[625],[574,4085,2692],{"className":4086},[2691],[574,4088,2771],{"className":4089},[625],[574,4091],{"className":4092,"style":922},[921],[574,4094,1467],{"className":4095},[926],[574,4097],{"className":4098,"style":922},[921],[574,4100,895],{"className":4101},[625],[574,4103,4105],{"className":4104},[625],[574,4106,2692],{"className":4107},[2691],[574,4109,3721],{"className":4110},[625],[574,4112,4113,4116],{"style":2699},[574,4114],{"className":4115,"style":646},[645],[574,4117,4119,4122,4128,4131,4134,4137,4140,4143,4149,4152,4155,4158,4161,4164,4170,4173,4176,4179,4182,4185,4191],{"className":4118},[625],[574,4120,895],{"className":4121},[625],[574,4123,4125],{"className":4124},[625],[574,4126,2692],{"className":4127},[2691],[574,4129,2718],{"className":4130},[625],[574,4132],{"className":4133,"style":922},[921],[574,4135,1467],{"className":4136},[926],[574,4138],{"className":4139,"style":922},[921],[574,4141,895],{"className":4142},[625],[574,4144,4146],{"className":4145},[625],[574,4147,2692],{"className":4148},[2691],[574,4150,3617],{"className":4151},[625],[574,4153],{"className":4154,"style":922},[921],[574,4156,1823],{"className":4157},[926],[574,4159],{"className":4160,"style":922},[921],[574,4162,895],{"className":4163},[625],[574,4165,4167],{"className":4166},[625],[574,4168,2692],{"className":4169},[2691],[574,4171,2792],{"className":4172},[625],[574,4174],{"className":4175,"style":922},[921],[574,4177,1467],{"className":4178},[926],[574,4180],{"className":4181,"style":922},[921],[574,4183,895],{"className":4184},[625],[574,4186,4188],{"className":4187},[625],[574,4189,2692],{"className":4190},[2691],[574,4192,3721],{"className":4193},[625],[574,4195,1159],{"className":4196},[1158],[574,4198,4200],{"className":4199},[634],[574,4201,4203],{"className":4202,"style":2728},[638],[574,4204],{},[574,4206,4208],{"className":4207,"style":2033},[943,2032],[574,4209,877],{"className":4210},[2037,1150],[574,4212],{"className":4213,"style":986},[921],[574,4215,890],{"className":4216},[990],[574,4218],{"className":4219,"style":986},[921],[574,4221,4223,4226],{"className":4222},[616],[574,4224],{"className":4225,"style":2644},[620],[574,4227,4229,4235,4304],{"className":4228},[2028],[574,4230,4232],{"className":4231,"style":2033},[914,2032],[574,4233,865],{"className":4234},[2037,1150],[574,4236,4238],{"className":4237},[625],[574,4239,4241],{"className":4240},[1915],[574,4242,4244],{"className":4243},[2048],[574,4245,4247,4296],{"className":4246},[630,1130],[574,4248,4250,4293],{"className":4249},[634],[574,4251,4253,4273],{"className":4252,"style":2672},[638],[574,4254,4255,4258],{"style":2675},[574,4256],{"className":4257,"style":646},[645],[574,4259,4261,4264,4270],{"className":4260},[625],[574,4262,895],{"className":4263},[625],[574,4265,4267],{"className":4266},[625],[574,4268,2692],{"className":4269},[2691],[574,4271,3617],{"className":4272},[625],[574,4274,4275,4278],{"style":2699},[574,4276],{"className":4277,"style":646},[645],[574,4279,4281,4284,4290],{"className":4280},[625],[574,4282,895],{"className":4283},[625],[574,4285,4287],{"className":4286},[625],[574,4288,2692],{"className":4289},[2691],[574,4291,3721],{"className":4292},[625],[574,4294,1159],{"className":4295},[1158],[574,4297,4299],{"className":4298},[634],[574,4300,4302],{"className":4301,"style":2728},[638],[574,4303],{},[574,4305,4307],{"className":4306,"style":2033},[943,2032],[574,4308,877],{"className":4309},[2037,1150],[565,4311,4312,4313,4356,4357,4482],{},"Langfristig hat Anbieter X also ",[574,4314,4316,4337],{"className":4315},[577],[574,4317,4319],{"className":4318},[581],[583,4320,4321],{"xmlns":585},[587,4322,4323,4334],{},[590,4324,4325,4328,4330],{},[828,4326,4327],{},"60",[879,4329,881],{},[597,4331,4333],{"mathvariant":4332},"normal","%",[605,4335,4336],{"encoding":607},"60\\,\\%",[574,4338,4340],{"className":4339,"ariaHidden":595},[612],[574,4341,4343,4347,4350,4353],{"className":4342},[616],[574,4344],{"className":4345,"style":4346},[620],"height:0.8056em;vertical-align:-0.0556em;",[574,4348,4327],{"className":4349},[625],[574,4351],{"className":4352,"style":947},[921],[574,4354,4333],{"className":4355},[625]," Marktanteil, egal wie die Anteile am Anfang verteilt sind. Der zweite Eigenwert ist ",[574,4358,4360,4387],{"className":4359},[577],[574,4361,4363],{"className":4362},[581],[583,4364,4365],{"xmlns":585},[587,4366,4367,4384],{},[590,4368,4369,4371,4373,4375,4377,4379,4381],{},[828,4370,830],{},[601,4372,871],{},[828,4374,2604],{},[601,4376,871],{},[828,4378,2595],{},[601,4380,890],{},[828,4382,4383],{},"0,5",[605,4385,4386],{"encoding":607},"1 - 0{,}2 - 0{,}3 = 0{,}5",[574,4388,4390,4409,4436,4463],{"className":4389,"ariaHidden":595},[612],[574,4391,4393,4397,4400,4403,4406],{"className":4392},[616],[574,4394],{"className":4395,"style":4396},[620],"height:0.7278em;vertical-align:-0.0833em;",[574,4398,830],{"className":4399},[625],[574,4401],{"className":4402,"style":922},[921],[574,4404,871],{"className":4405},[926],[574,4407],{"className":4408,"style":922},[921],[574,4410,4412,4415,4418,4424,4427,4430,4433],{"className":4411},[616],[574,4413],{"className":4414,"style":3026},[620],[574,4416,895],{"className":4417},[625],[574,4419,4421],{"className":4420},[625],[574,4422,2692],{"className":4423},[2691],[574,4425,2718],{"className":4426},[625],[574,4428],{"className":4429,"style":922},[921],[574,4431,871],{"className":4432},[926],[574,4434],{"className":4435,"style":922},[921],[574,4437,4439,4442,4445,4451,4454,4457,4460],{"className":4438},[616],[574,4440],{"className":4441,"style":3026},[620],[574,4443,895],{"className":4444},[625],[574,4446,4448],{"className":4447},[625],[574,4449,2692],{"className":4450},[2691],[574,4452,2771],{"className":4453},[625],[574,4455],{"className":4456,"style":986},[921],[574,4458,890],{"className":4459},[990],[574,4461],{"className":4462,"style":986},[921],[574,4464,4466,4469,4472,4478],{"className":4465},[616],[574,4467],{"className":4468,"style":3026},[620],[574,4470,895],{"className":4471},[625],[574,4473,4475],{"className":4474},[625],[574,4476,2692],{"className":4477},[2691],[574,4479,4481],{"className":4480},[625],"5",", deshalb halbiert sich der Abstand zur stationären Verteilung mit jedem Schritt.",[565,4484,4485,4486,4685,4686,4821,4822,4879,4880,4908],{},"Gegenbeispiel zur Konvergenz: Bei ",[574,4487,4489,4541],{"className":4488},[577],[574,4490,4492],{"className":4491},[581],[583,4493,4494],{"xmlns":585},[587,4495,4496,4538],{},[590,4497,4498,4500,4502],{},[597,4499,868],{},[601,4501,890],{},[590,4503,4504,4506,4536],{},[601,4505,865],{"fence":595},[1915,4507,4508,4522],{"rowspacing":1917,"columnalign":2579,"columnspacing":1919},[1921,4509,4510,4516],{},[1924,4511,4512],{},[1927,4513,4514],{"scriptlevel":895,"displaystyle":864},[828,4515,895],{},[1924,4517,4518],{},[1927,4519,4520],{"scriptlevel":895,"displaystyle":864},[828,4521,830],{},[1921,4523,4524,4530],{},[1924,4525,4526],{},[1927,4527,4528],{"scriptlevel":895,"displaystyle":864},[828,4529,830],{},[1924,4531,4532],{},[1927,4533,4534],{"scriptlevel":895,"displaystyle":864},[828,4535,895],{},[601,4537,877],{"fence":595},[605,4539,4540],{"encoding":607},"A = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}",[574,4542,4544,4562],{"className":4543,"ariaHidden":595},[612],[574,4545,4547,4550,4553,4556,4559],{"className":4546},[616],[574,4548],{"className":4549,"style":1063},[620],[574,4551,868],{"className":4552},[625,650],[574,4554],{"className":4555,"style":986},[921],[574,4557,890],{"className":4558},[990],[574,4560],{"className":4561,"style":986},[921],[574,4563,4565,4568],{"className":4564},[616],[574,4566],{"className":4567,"style":2644},[620],[574,4569,4571,4577,4679],{"className":4570},[2028],[574,4572,4574],{"className":4573,"style":2033},[914,2032],[574,4575,865],{"className":4576},[2037,1150],[574,4578,4580],{"className":4579},[625],[574,4581,4583,4628,4631,4634],{"className":4582},[1915],[574,4584,4586],{"className":4585},[2048],[574,4587,4589,4620],{"className":4588},[630,1130],[574,4590,4592,4617],{"className":4591},[634],[574,4593,4595,4606],{"className":4594,"style":2672},[638],[574,4596,4597,4600],{"style":2675},[574,4598],{"className":4599,"style":646},[645],[574,4601,4603],{"className":4602},[625],[574,4604,895],{"className":4605},[625],[574,4607,4608,4611],{"style":2699},[574,4609],{"className":4610,"style":646},[645],[574,4612,4614],{"className":4613},[625],[574,4615,830],{"className":4616},[625],[574,4618,1159],{"className":4619},[1158],[574,4621,4623],{"className":4622},[634],[574,4624,4626],{"className":4625,"style":2728},[638],[574,4627],{},[574,4629],{"className":4630,"style":2735},[2734],[574,4632],{"className":4633,"style":2735},[2734],[574,4635,4637],{"className":4636},[2048],[574,4638,4640,4671],{"className":4639},[630,1130],[574,4641,4643,4668],{"className":4642},[634],[574,4644,4646,4657],{"className":4645,"style":2672},[638],[574,4647,4648,4651],{"style":2675},[574,4649],{"className":4650,"style":646},[645],[574,4652,4654],{"className":4653},[625],[574,4655,830],{"className":4656},[625],[574,4658,4659,4662],{"style":2699},[574,4660],{"className":4661,"style":646},[645],[574,4663,4665],{"className":4664},[625],[574,4666,895],{"className":4667},[625],[574,4669,1159],{"className":4670},[1158],[574,4672,4674],{"className":4673},[634],[574,4675,4677],{"className":4676,"style":2728},[638],[574,4678],{},[574,4680,4682],{"className":4681,"style":2033},[943,2032],[574,4683,877],{"className":4684},[2037,1150]," ist ",[574,4687,4689,4723],{"className":4688},[577],[574,4690,4692],{"className":4691},[581],[583,4693,4694],{"xmlns":585},[587,4695,4696,4720],{},[590,4697,4698,4704,4706,4708,4710,4713,4716,4718],{},[593,4699,4700,4702],{"accent":595},[597,4701,599],{},[601,4703,603],{},[601,4705,890],{},[601,4707,865],{"stretchy":864},[828,4709,4383],{},[601,4711,4712],{"separator":595},";",[879,4714,4715],{}," ",[828,4717,4383],{},[601,4719,877],{"stretchy":864},[605,4721,4722],{"encoding":607},"\\vec{\\pi} = (0{,}5;\\ 0{,}5)",[574,4724,4726,4776],{"className":4725,"ariaHidden":595},[612],[574,4727,4729,4732,4767,4770,4773],{"className":4728},[616],[574,4730],{"className":4731,"style":621},[620],[574,4733,4735],{"className":4734},[625,626],[574,4736,4738],{"className":4737},[630],[574,4739,4741],{"className":4740},[634],[574,4742,4744,4752],{"className":4743,"style":621},[638],[574,4745,4746,4749],{"style":641},[574,4747],{"className":4748,"style":646},[645],[574,4750,599],{"className":4751,"style":651},[625,650],[574,4753,4754,4757],{"style":641},[574,4755],{"className":4756,"style":646},[645],[574,4758,4760],{"className":4759,"style":661},[660],[574,4761,4763],{"className":4762,"style":666},[665],[668,4764,4765],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,4766],{"d":679},[574,4768],{"className":4769,"style":986},[921],[574,4771,890],{"className":4772},[990],[574,4774],{"className":4775,"style":986},[921],[574,4777,4779,4782,4785,4788,4794,4797,4800,4803,4806,4809,4815,4818],{"className":4778},[616],[574,4780],{"className":4781,"style":910},[620],[574,4783,865],{"className":4784},[914],[574,4786,895],{"className":4787},[625],[574,4789,4791],{"className":4790},[625],[574,4792,2692],{"className":4793},[2691],[574,4795,4481],{"className":4796},[625],[574,4798,4712],{"className":4799},[2691],[574,4801,4715],{"className":4802},[921],[574,4804],{"className":4805,"style":947},[921],[574,4807,895],{"className":4808},[625],[574,4810,4812],{"className":4811},[625],[574,4813,2692],{"className":4814},[2691],[574,4816,4481],{"className":4817},[625],[574,4819,877],{"className":4820},[943]," stationär, aber vom Start ",[574,4823,4825,4849],{"className":4824},[577],[574,4826,4828],{"className":4827},[581],[583,4829,4830],{"xmlns":585},[587,4831,4832,4846],{},[590,4833,4834,4836,4838,4840,4842,4844],{},[601,4835,865],{"stretchy":864},[828,4837,830],{},[601,4839,4712],{"separator":595},[879,4841,4715],{},[828,4843,895],{},[601,4845,877],{"stretchy":864},[605,4847,4848],{"encoding":607},"(1;\\ 0)",[574,4850,4852],{"className":4851,"ariaHidden":595},[612],[574,4853,4855,4858,4861,4864,4867,4870,4873,4876],{"className":4854},[616],[574,4856],{"className":4857,"style":910},[620],[574,4859,865],{"className":4860},[914],[574,4862,830],{"className":4863},[625],[574,4865,4712],{"className":4866},[2691],[574,4868,4715],{"className":4869},[921],[574,4871],{"className":4872,"style":947},[921],[574,4874,895],{"className":4875},[625],[574,4877,877],{"className":4878},[943]," aus springt die Verteilung ewig hin und her (Periode ",[574,4881,4883,4896],{"className":4882},[577],[574,4884,4886],{"className":4885},[581],[583,4887,4888],{"xmlns":585},[587,4889,4890,4894],{},[590,4891,4892],{},[828,4893,2718],{},[605,4895,2718],{"encoding":607},[574,4897,4899],{"className":4898,"ariaHidden":595},[612],[574,4900,4902,4905],{"className":4901},[616],[574,4903],{"className":4904,"style":842},[620],[574,4906,2718],{"className":4907},[625],").",[560,4910,4912],{"id":4911},"typische-fehler","Typische Fehler",[1357,4914,4915,5110,5449,5517],{},[1360,4916,4917,4918,5045,5046,846],{},"Die Normierung vergessen. ",[574,4919,4921,4948],{"className":4920},[577],[574,4922,4924],{"className":4923},[581],[583,4925,4926],{"xmlns":585},[587,4927,4928,4946],{},[590,4929,4930,4932,4938,4940],{},[597,4931,868],{},[593,4933,4934,4936],{"accent":595},[597,4935,599],{},[601,4937,603],{},[601,4939,890],{},[593,4941,4942,4944],{"accent":595},[597,4943,599],{},[601,4945,603],{},[605,4947,2841],{"encoding":607},[574,4949,4951,5004],{"className":4950,"ariaHidden":595},[612],[574,4952,4954,4957,4960,4995,4998,5001],{"className":4953},[616],[574,4955],{"className":4956,"style":621},[620],[574,4958,868],{"className":4959},[625,650],[574,4961,4963],{"className":4962},[625,626],[574,4964,4966],{"className":4965},[630],[574,4967,4969],{"className":4968},[634],[574,4970,4972,4980],{"className":4971,"style":621},[638],[574,4973,4974,4977],{"style":641},[574,4975],{"className":4976,"style":646},[645],[574,4978,599],{"className":4979,"style":651},[625,650],[574,4981,4982,4985],{"style":641},[574,4983],{"className":4984,"style":646},[645],[574,4986,4988],{"className":4987,"style":661},[660],[574,4989,4991],{"className":4990,"style":666},[665],[668,4992,4993],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,4994],{"d":679},[574,4996],{"className":4997,"style":986},[921],[574,4999,890],{"className":5000},[990],[574,5002],{"className":5003,"style":986},[921],[574,5005,5007,5010],{"className":5006},[616],[574,5008],{"className":5009,"style":621},[620],[574,5011,5013],{"className":5012},[625,626],[574,5014,5016],{"className":5015},[630],[574,5017,5019],{"className":5018},[634],[574,5020,5022,5030],{"className":5021,"style":621},[638],[574,5023,5024,5027],{"style":641},[574,5025],{"className":5026,"style":646},[645],[574,5028,599],{"className":5029,"style":651},[625,650],[574,5031,5032,5035],{"style":641},[574,5033],{"className":5034,"style":646},[645],[574,5036,5038],{"className":5037,"style":661},[660],[574,5039,5041],{"className":5040,"style":666},[665],[668,5042,5043],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,5044],{"d":679}," allein hat unendlich viele Lösungen, alle Vielfachen von ",[574,5047,5049,5066],{"className":5048},[577],[574,5050,5052],{"className":5051},[581],[583,5053,5054],{"xmlns":585},[587,5055,5056,5064],{},[590,5057,5058],{},[593,5059,5060,5062],{"accent":595},[597,5061,599],{},[601,5063,603],{},[605,5065,608],{"encoding":607},[574,5067,5069],{"className":5068,"ariaHidden":595},[612],[574,5070,5072,5075],{"className":5071},[616],[574,5073],{"className":5074,"style":621},[620],[574,5076,5078],{"className":5077},[625,626],[574,5079,5081],{"className":5080},[630],[574,5082,5084],{"className":5083},[634],[574,5085,5087,5095],{"className":5086,"style":621},[638],[574,5088,5089,5092],{"style":641},[574,5090],{"className":5091,"style":646},[645],[574,5093,599],{"className":5094,"style":651},[625,650],[574,5096,5097,5100],{"style":641},[574,5098],{"className":5099,"style":646},[645],[574,5101,5103],{"className":5102,"style":661},[660],[574,5104,5106],{"className":5105,"style":666},[665],[668,5107,5108],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,5109],{"d":679},[1360,5111,5112,5113,5320,5321,846],{},"Mit der falschen Konvention rechnen: Bei zeilenstochastischen Matrizen ist ",[574,5114,5116,5159],{"className":5115},[577],[574,5117,5119],{"className":5118},[581],[583,5120,5121],{"xmlns":585},[587,5122,5123,5157],{},[590,5124,5125,5139,5141,5143],{},[1394,5126,5127,5133],{},[593,5128,5129,5131],{"accent":595},[597,5130,599],{},[601,5132,603],{},[590,5134,5135,5137],{},[879,5136,881],{},[597,5138,2281],{},[597,5140,2284],{},[601,5142,890],{},[1394,5144,5145,5151],{},[593,5146,5147,5149],{"accent":595},[597,5148,599],{},[601,5150,603],{},[590,5152,5153,5155],{},[879,5154,881],{},[597,5156,2281],{},[605,5158,2303],{"encoding":607},[574,5160,5162,5247],{"className":5161,"ariaHidden":595},[612],[574,5163,5165,5168,5235,5238,5241,5244],{"className":5164},[616],[574,5166],{"className":5167,"style":2313},[620],[574,5169,5171,5206],{"className":5170},[625],[574,5172,5174],{"className":5173},[625,626],[574,5175,5177],{"className":5176},[630],[574,5178,5180],{"className":5179},[634],[574,5181,5183,5191],{"className":5182,"style":621},[638],[574,5184,5185,5188],{"style":641},[574,5186],{"className":5187,"style":646},[645],[574,5189,599],{"className":5190,"style":651},[625,650],[574,5192,5193,5196],{"style":641},[574,5194],{"className":5195,"style":646},[645],[574,5197,5199],{"className":5198,"style":661},[660],[574,5200,5202],{"className":5201,"style":666},[665],[668,5203,5204],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,5205],{"d":679},[574,5207,5209],{"className":5208},[1126],[574,5210,5212],{"className":5211},[630],[574,5213,5215],{"className":5214},[634],[574,5216,5218],{"className":5217,"style":2313},[638],[574,5219,5220,5223],{"style":1434},[574,5221],{"className":5222,"style":1144},[645],[574,5224,5226],{"className":5225},[1148,1149,1150,1151],[574,5227,5229,5232],{"className":5228},[625,1151],[574,5230],{"className":5231,"style":2378},[921,1151],[574,5233,2281],{"className":5234,"style":2382},[625,650,1151],[574,5236,2284],{"className":5237,"style":2382},[625,650],[574,5239],{"className":5240,"style":986},[921],[574,5242,890],{"className":5243},[990],[574,5245],{"className":5246,"style":986},[921],[574,5248,5250,5253],{"className":5249},[616],[574,5251],{"className":5252,"style":2313},[620],[574,5254,5256,5291],{"className":5255},[625],[574,5257,5259],{"className":5258},[625,626],[574,5260,5262],{"className":5261},[630],[574,5263,5265],{"className":5264},[634],[574,5266,5268,5276],{"className":5267,"style":621},[638],[574,5269,5270,5273],{"style":641},[574,5271],{"className":5272,"style":646},[645],[574,5274,599],{"className":5275,"style":651},[625,650],[574,5277,5278,5281],{"style":641},[574,5279],{"className":5280,"style":646},[645],[574,5282,5284],{"className":5283,"style":661},[660],[574,5285,5287],{"className":5286,"style":666},[665],[668,5288,5289],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,5290],{"d":679},[574,5292,5294],{"className":5293},[1126],[574,5295,5297],{"className":5296},[630],[574,5298,5300],{"className":5299},[634],[574,5301,5303],{"className":5302,"style":2313},[638],[574,5304,5305,5308],{"style":1434},[574,5306],{"className":5307,"style":1144},[645],[574,5309,5311],{"className":5310},[1148,1149,1150,1151],[574,5312,5314,5317],{"className":5313},[625,1151],[574,5315],{"className":5316,"style":2378},[921,1151],[574,5318,2281],{"className":5319,"style":2382},[625,650,1151]," zu lösen, nicht ",[574,5322,5324,5352],{"className":5323},[577],[574,5325,5327],{"className":5326},[581],[583,5328,5329],{"xmlns":585},[587,5330,5331,5349],{},[590,5332,5333,5335,5341,5343],{},[597,5334,2284],{},[593,5336,5337,5339],{"accent":595},[597,5338,599],{},[601,5340,603],{},[601,5342,890],{},[593,5344,5345,5347],{"accent":595},[597,5346,599],{},[601,5348,603],{},[605,5350,5351],{"encoding":607},"P\\vec{\\pi} = \\vec{\\pi}",[574,5353,5355,5408],{"className":5354,"ariaHidden":595},[612],[574,5356,5358,5361,5364,5399,5402,5405],{"className":5357},[616],[574,5359],{"className":5360,"style":621},[620],[574,5362,2284],{"className":5363,"style":2382},[625,650],[574,5365,5367],{"className":5366},[625,626],[574,5368,5370],{"className":5369},[630],[574,5371,5373],{"className":5372},[634],[574,5374,5376,5384],{"className":5375,"style":621},[638],[574,5377,5378,5381],{"style":641},[574,5379],{"className":5380,"style":646},[645],[574,5382,599],{"className":5383,"style":651},[625,650],[574,5385,5386,5389],{"style":641},[574,5387],{"className":5388,"style":646},[645],[574,5390,5392],{"className":5391,"style":661},[660],[574,5393,5395],{"className":5394,"style":666},[665],[668,5396,5397],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,5398],{"d":679},[574,5400],{"className":5401,"style":986},[921],[574,5403,890],{"className":5404},[990],[574,5406],{"className":5407,"style":986},[921],[574,5409,5411,5414],{"className":5410},[616],[574,5412],{"className":5413,"style":621},[620],[574,5415,5417],{"className":5416},[625,626],[574,5418,5420],{"className":5419},[630],[574,5421,5423],{"className":5422},[634],[574,5424,5426,5434],{"className":5425,"style":621},[638],[574,5427,5428,5431],{"style":641},[574,5429],{"className":5430,"style":646},[645],[574,5432,599],{"className":5433,"style":651},[625,650],[574,5435,5436,5439],{"style":641},[574,5437],{"className":5438,"style":646},[645],[574,5440,5442],{"className":5441,"style":661},[660],[574,5443,5445],{"className":5444,"style":666},[665],[668,5446,5447],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,5448],{"d":679},[1360,5450,5451,5452,5516],{},"Annehmen, die Kette konvergiere immer gegen ",[574,5453,5455,5472],{"className":5454},[577],[574,5456,5458],{"className":5457},[581],[583,5459,5460],{"xmlns":585},[587,5461,5462,5470],{},[590,5463,5464],{},[593,5465,5466,5468],{"accent":595},[597,5467,599],{},[601,5469,603],{},[605,5471,608],{"encoding":607},[574,5473,5475],{"className":5474,"ariaHidden":595},[612],[574,5476,5478,5481],{"className":5477},[616],[574,5479],{"className":5480,"style":621},[620],[574,5482,5484],{"className":5483},[625,626],[574,5485,5487],{"className":5486},[630],[574,5488,5490],{"className":5489},[634],[574,5491,5493,5501],{"className":5492,"style":621},[638],[574,5494,5495,5498],{"style":641},[574,5496],{"className":5497,"style":646},[645],[574,5499,599],{"className":5500,"style":651},[625,650],[574,5502,5503,5506],{"style":641},[574,5504],{"className":5505,"style":646},[645],[574,5507,5509],{"className":5508,"style":661},[660],[574,5510,5512],{"className":5511,"style":666},[665],[668,5513,5514],{"xmlns":670,"width":671,"height":672,"style":673,"viewBox":674,"preserveAspectRatio":675},[677,5515],{"d":679},". Bei periodischen Ketten gilt das nicht.",[1360,5518,5519],{},"Bei reduziblen Ketten eine eindeutige stationäre Verteilung erwarten.",{"title":5521,"searchDepth":5522,"depth":5522,"links":5523},"",2,[5524,5525,5526],{"id":562,"depth":5522,"text":563},{"id":2552,"depth":5522,"text":2553},{"id":4911,"depth":5522,"text":4912},[5528,5531,5534,5536,5539,5542,5544,5546],{"lhs":5529,"rhs":5530},"0.8*0.6 + 0.3*0.4","0.6",{"lhs":5532,"rhs":5533},"0.2*0.6 + 0.7*0.4","0.4",{"lhs":5535,"rhs":5530},"0.3 \u002F (0.2 + 0.3)",{"lhs":5537,"rhs":5538},"(1 - a)*b\u002F(a + b) + b*a\u002F(a + b)","b\u002F(a + b)",{"lhs":5540,"rhs":5541},"a*b\u002F(a + b) + (1 - b)*a\u002F(a + b)","a\u002F(a + b)",{"lhs":5543,"rhs":5530},"round(multiply(pow([[0.8, 0.3], [0.2, 0.7]], 50), [1, 0])[1], 9)",{"lhs":5545,"rhs":5533},"round(multiply(pow([[0.8, 0.3], [0.2, 0.7]], 50), [0, 1])[2], 9)",{"lhs":5547,"rhs":5548},"1 - 0.2 - 0.3","0.5","A \\text{ stochastische Matrix (Spaltensummen } 1),\\ \\pi_i \\geq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stochastische Matrix (Spaltensummen\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>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>i\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\pi_i \\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:0.786em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\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:-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\">i\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","stationary-distribution","A \\cdot \\vec{\\pi} = \\vec{\\pi}, \\qquad \\pi_1 + \\ldots + \\pi_m = 1","\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>\u003Cmover accent=\"true\">\u003Cmi>π\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>π\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsub>\u003Cmi>π\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>π\u003C\u002Fmi>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\cdot \\vec{\\pi} = \\vec{\\pi}, \\qquad \\pi_1 + \\ldots + \\pi_m = 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:0.6833em;\">\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:0.714em;\">\u003C\u002Fspan>\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;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\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=\"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:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\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;\">π\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\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=\"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 mathnormal\" style=\"margin-right:0.0359em;\">π\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=\"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:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">π\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\">m\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstationaere-verteilung",[],[5562,5563,5564,5565],"markov-chain","gaussian-elimination","characteristic-polynomial","matrix-multiplication",{"title":548,"description":5521},"de\u002Fformulas\u002Fmath\u002Fstochastics\u002Fstationaere-verteilung","Eine stationäre Verteilung ist ein Wahrscheinlichkeitsvektor, den die Übergangsmatrix unverändert lässt; oft ist sie die Grenzverteilung.",[5570,5571,5572,5573,5574],"markow-kette","fixvektor","grenzverteilung","eigenvektor","übergangsmatrix",[5576,5579,5582,5586],{"symbol":868,"meaning":5577,"symbolHtml":5578},"Übergangsmatrix; a_ij ist die Wahrscheinlichkeit für einen Wechsel von Zustand j nach Zustand i","\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>",{"symbol":608,"meaning":5580,"symbolHtml":5581},"stationäre Verteilung (Fixvektor), die sich durch einen Schritt nicht ändert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>π\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation 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