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C^T",[573,1087,1089,1111,1159,1204],{"className":1088,"ariaHidden":610},[609],[573,1090,1092,1096,1099,1102,1105,1108],{"className":1091},[614],[573,1093],{"className":1094,"style":1095},[618],"height:1em;vertical-align:-0.25em;",[573,1097,921],{"className":1098},[956],[573,1100,597],{"className":1101},[623,627],[573,1103],{"className":1104,"style":706},[705],[573,1106,1057],{"className":1107},[710],[573,1109],{"className":1110,"style":706},[705],[573,1112,1114,1117,1121,1150,1153,1156],{"className":1113},[614],[573,1115],{"className":1116,"style":952},[618],[573,1118,1060],{"className":1119,"style":1120},[623,627],"margin-right:0.0715em;",[573,1122,1124,1127],{"className":1123},[989],[573,1125,932],{"className":1126},[989],[573,1128,1130],{"className":1129},[631],[573,1131,1133],{"className":1132},[635],[573,1134,1136],{"className":1135},[639],[573,1137,1139],{"className":1138,"style":619},[643],[573,1140,1141,1144],{"style":646},[573,1142],{"className":1143,"style":651},[650],[573,1145,1147],{"className":1146},[655,656,657,658],[573,1148,600],{"className":1149,"style":662},[623,627,658],[573,1151],{"className":1152,"style":1019},[705],[573,1154,937],{"className":1155},[1023],[573,1157],{"className":1158,"style":1019},[705],[573,1160,1162,1166,1195,1198,1201],{"className":1161},[614],[573,1163],{"className":1164,"style":1165},[618],"height:0.9247em;vertical-align:-0.0833em;",[573,1167,1169,1172],{"className":1168},[623],[573,1170,597],{"className":1171},[623,627],[573,1173,1175],{"className":1174},[631],[573,1176,1178],{"className":1177},[635],[573,1179,1181],{"className":1180},[639],[573,1182,1184],{"className":1183,"style":619},[643],[573,1185,1186,1189],{"style":646},[573,1187],{"className":1188,"style":651},[650],[573,1190,1192],{"className":1191},[655,656,657,658],[573,1193,600],{"className":1194,"style":662},[623,627,658],[573,1196],{"className":1197,"style":706},[705],[573,1199,1057],{"className":1200},[710],[573,1202],{"className":1203,"style":706},[705],[573,1205,1207,1210],{"className":1206},[614],[573,1208],{"className":1209,"style":619},[618],[573,1211,1213,1216],{"className":1212},[623],[573,1214,1060],{"className":1215,"style":1120},[623,627],[573,1217,1219],{"className":1218},[631],[573,1220,1222],{"className":1221},[635],[573,1223,1225],{"className":1224},[639],[573,1226,1228],{"className":1227,"style":619},[643],[573,1229,1230,1233],{"style":646},[573,1231],{"className":1232,"style":651},[650],[573,1234,1236],{"className":1235},[655,656,657,658],[573,1237,600],{"className":1238,"style":662},[623,627,658]," und ",[573,1241,1243,1278],{"className":1242},[576],[573,1244,1246],{"className":1245},[580],[582,1247,1248],{"xmlns":584},[586,1249,1250,1275],{},[589,1251,1252,1254,1257,1259,1265,1267,1269],{},[680,1253,921],{"stretchy":920},[595,1255,1256],{},"λ",[595,1258,597],{},[592,1260,1261,1263],{},[680,1262,932],{"stretchy":920},[595,1264,600],{},[680,1266,937],{},[595,1268,1256],{},[592,1270,1271,1273],{},[595,1272,597],{},[595,1274,600],{},[602,1276,1277],{"encoding":604},"(\\lambda A)^T = \\lambda A^T",[573,1279,1281,1334],{"className":1280,"ariaHidden":610},[609],[573,1282,1284,1287,1290,1293,1296,1325,1328,1331],{"className":1283},[614],[573,1285],{"className":1286,"style":952},[618],[573,1288,921],{"className":1289},[956],[573,1291,1256],{"className":1292},[623,627],[573,1294,597],{"className":1295},[623,627],[573,1297,1299,1302],{"className":1298},[989],[573,1300,932],{"className":1301},[989],[573,1303,1305],{"className":1304},[631],[573,1306,1308],{"className":1307},[635],[573,1309,1311],{"className":1310},[639],[573,1312,1314],{"className":1313,"style":619},[643],[573,1315,1316,1319],{"style":646},[573,1317],{"className":1318,"style":651},[650],[573,1320,1322],{"className":1321},[655,656,657,658],[573,1323,600],{"className":1324,"style":662},[623,627,658],[573,1326],{"className":1327,"style":1019},[705],[573,1329,937],{"className":1330},[1023],[573,1332],{"className":1333,"style":1019},[705],[573,1335,1337,1340,1343],{"className":1336},[614],[573,1338],{"className":1339,"style":619},[618],[573,1341,1256],{"className":1342},[623,627],[573,1344,1346,1349],{"className":1345},[623],[573,1347,597],{"className":1348},[623,627],[573,1350,1352],{"className":1351},[631],[573,1353,1355],{"className":1354},[635],[573,1356,1358],{"className":1357},[639],[573,1359,1361],{"className":1360,"style":619},[643],[573,1362,1363,1366],{"style":646},[573,1364],{"className":1365,"style":651},[650],[573,1367,1369],{"className":1368},[655,656,657,658],[573,1370,600],{"className":1371,"style":662},[623,627,658],[904,1373,1374,1536,1537,1540,1541,896],{},[573,1375,1377,1415],{"className":1376},[576],[573,1378,1380],{"className":1379},[580],[582,1381,1382],{"xmlns":584},[586,1383,1384,1413],{},[589,1385,1386,1388,1390,1393,1399,1401,1407],{},[680,1387,921],{"stretchy":920},[595,1389,597],{},[595,1391,1392],{},"B",[592,1394,1395,1397],{},[680,1396,932],{"stretchy":920},[595,1398,600],{},[680,1400,937],{},[592,1402,1403,1405],{},[595,1404,1392],{},[595,1406,600],{},[592,1408,1409,1411],{},[595,1410,597],{},[595,1412,600],{},[602,1414,551],{"encoding":604},[573,1416,1418,1472],{"className":1417,"ariaHidden":610},[609],[573,1419,1421,1424,1427,1430,1434,1463,1466,1469],{"className":1420},[614],[573,1422],{"className":1423,"style":952},[618],[573,1425,921],{"className":1426},[956],[573,1428,597],{"className":1429},[623,627],[573,1431,1392],{"className":1432,"style":1433},[623,627],"margin-right:0.0502em;",[573,1435,1437,1440],{"className":1436},[989],[573,1438,932],{"className":1439},[989],[573,1441,1443],{"className":1442},[631],[573,1444,1446],{"className":1445},[635],[573,1447,1449],{"className":1448},[639],[573,1450,1452],{"className":1451,"style":619},[643],[573,1453,1454,1457],{"style":646},[573,1455],{"className":1456,"style":651},[650],[573,1458,1460],{"className":1459},[655,656,657,658],[573,1461,600],{"className":1462,"style":662},[623,627,658],[573,1464],{"className":1465,"style":1019},[705],[573,1467,937],{"className":1468},[1023],[573,1470],{"className":1471,"style":1019},[705],[573,1473,1475,1478,1507],{"className":1474},[614],[573,1476],{"className":1477,"style":619},[618],[573,1479,1481,1484],{"className":1480},[623],[573,1482,1392],{"className":1483,"style":1433},[623,627],[573,1485,1487],{"className":1486},[631],[573,1488,1490],{"className":1489},[635],[573,1491,1493],{"className":1492},[639],[573,1494,1496],{"className":1495,"style":619},[643],[573,1497,1498,1501],{"style":646},[573,1499],{"className":1500,"style":651},[650],[573,1502,1504],{"className":1503},[655,656,657,658],[573,1505,600],{"className":1506,"style":662},[623,627,658],[573,1508,1510,1513],{"className":1509},[623],[573,1511,597],{"className":1512},[623,627],[573,1514,1516],{"className":1515},[631],[573,1517,1519],{"className":1518},[635],[573,1520,1522],{"className":1521},[639],[573,1523,1525],{"className":1524,"style":619},[643],[573,1526,1527,1530],{"style":646},[573,1528],{"className":1529,"style":651},[650],[573,1531,1533],{"className":1532},[655,656,657,658],[573,1534,600],{"className":1535,"style":662},[623,627,658],": Die ",[568,1538,1539],{},"Reihenfolge kehrt sich um",". Bei mehreren Faktoren gilt ",[573,1542,1544,1590],{"className":1543},[576],[573,1545,1547],{"className":1546},[580],[582,1548,1549],{"xmlns":584},[586,1550,1551,1587],{},[589,1552,1553,1555,1557,1559,1561,1567,1569,1575,1581],{},[680,1554,921],{"stretchy":920},[595,1556,597],{},[595,1558,1392],{},[595,1560,1060],{},[592,1562,1563,1565],{},[680,1564,932],{"stretchy":920},[595,1566,600],{},[680,1568,937],{},[592,1570,1571,1573],{},[595,1572,1060],{},[595,1574,600],{},[592,1576,1577,1579],{},[595,1578,1392],{},[595,1580,600],{},[592,1582,1583,1585],{},[595,1584,597],{},[595,1586,600],{},[602,1588,1589],{"encoding":604},"(ABC)^T = C^T B^T A^T",[573,1591,1593,1649],{"className":1592,"ariaHidden":610},[609],[573,1594,1596,1599,1602,1605,1608,1611,1640,1643,1646],{"className":1595},[614],[573,1597],{"className":1598,"style":952},[618],[573,1600,921],{"className":1601},[956],[573,1603,597],{"className":1604},[623,627],[573,1606,1392],{"className":1607,"style":1433},[623,627],[573,1609,1060],{"className":1610,"style":1120},[623,627],[573,1612,1614,1617],{"className":1613},[989],[573,1615,932],{"className":1616},[989],[573,1618,1620],{"className":1619},[631],[573,1621,1623],{"className":1622},[635],[573,1624,1626],{"className":1625},[639],[573,1627,1629],{"className":1628,"style":619},[643],[573,1630,1631,1634],{"style":646},[573,1632],{"className":1633,"style":651},[650],[573,1635,1637],{"className":1636},[655,656,657,658],[573,1638,600],{"className":1639,"style":662},[623,627,658],[573,1641],{"className":1642,"style":1019},[705],[573,1644,937],{"className":1645},[1023],[573,1647],{"className":1648,"style":1019},[705],[573,1650,1652,1655,1684,1713],{"className":1651},[614],[573,1653],{"className":1654,"style":619},[618],[573,1656,1658,1661],{"className":1657},[623],[573,1659,1060],{"className":1660,"style":1120},[623,627],[573,1662,1664],{"className":1663},[631],[573,1665,1667],{"className":1666},[635],[573,1668,1670],{"className":1669},[639],[573,1671,1673],{"className":1672,"style":619},[643],[573,1674,1675,1678],{"style":646},[573,1676],{"className":1677,"style":651},[650],[573,1679,1681],{"className":1680},[655,656,657,658],[573,1682,600],{"className":1683,"style":662},[623,627,658],[573,1685,1687,1690],{"className":1686},[623],[573,1688,1392],{"className":1689,"style":1433},[623,627],[573,1691,1693],{"className":1692},[631],[573,1694,1696],{"className":1695},[635],[573,1697,1699],{"className":1698},[639],[573,1700,1702],{"className":1701,"style":619},[643],[573,1703,1704,1707],{"style":646},[573,1705],{"className":1706,"style":651},[650],[573,1708,1710],{"className":1709},[655,656,657,658],[573,1711,600],{"className":1712,"style":662},[623,627,658],[573,1714,1716,1719],{"className":1715},[623],[573,1717,597],{"className":1718},[623,627],[573,1720,1722],{"className":1721},[631],[573,1723,1725],{"className":1724},[635],[573,1726,1728],{"className":1727},[639],[573,1729,1731],{"className":1730,"style":619},[643],[573,1732,1733,1736],{"style":646},[573,1734],{"className":1735,"style":651},[650],[573,1737,1739],{"className":1738},[655,656,657,658],[573,1740,600],{"className":1741,"style":662},[623,627,658],[904,1743,1744,1959,1960,896],{},[573,1745,1747,1800],{"className":1746},[576],[573,1748,1750],{"className":1749},[580],[582,1751,1752],{"xmlns":584},[586,1753,1754,1797],{},[589,1755,1756,1758,1771,1777,1779,1781,1787],{},[680,1757,921],{"stretchy":920},[592,1759,1760,1762],{},[595,1761,597],{},[589,1763,1764,1767],{},[680,1765,1766],{},"−",[1768,1769,1770],"mn",{},"1",[592,1772,1773,1775],{},[680,1774,932],{"stretchy":920},[595,1776,600],{},[680,1778,937],{},[680,1780,921],{"stretchy":920},[592,1782,1783,1785],{},[595,1784,597],{},[595,1786,600],{},[592,1788,1789,1791],{},[680,1790,932],{"stretchy":920},[589,1792,1793,1795],{},[680,1794,1766],{},[1768,1796,1770],{},[602,1798,1799],{"encoding":604},"(A^{-1})^T = (A^T)^{-1}",[573,1801,1803,1886],{"className":1802,"ariaHidden":610},[609],[573,1804,1806,1809,1812,1848,1877,1880,1883],{"className":1805},[614],[573,1807],{"className":1808,"style":952},[618],[573,1810,921],{"className":1811},[956],[573,1813,1815,1818],{"className":1814},[623],[573,1816,597],{"className":1817},[623,627],[573,1819,1821],{"className":1820},[631],[573,1822,1824],{"className":1823},[635],[573,1825,1827],{"className":1826},[639],[573,1828,1831],{"className":1829,"style":1830},[643],"height:0.8141em;",[573,1832,1833,1836],{"style":646},[573,1834],{"className":1835,"style":651},[650],[573,1837,1839],{"className":1838},[655,656,657,658],[573,1840,1842,1845],{"className":1841},[623,658],[573,1843,1766],{"className":1844},[623,658],[573,1846,1770],{"className":1847},[623,658],[573,1849,1851,1854],{"className":1850},[989],[573,1852,932],{"className":1853},[989],[573,1855,1857],{"className":1856},[631],[573,1858,1860],{"className":1859},[635],[573,1861,1863],{"className":1862},[639],[573,1864,1866],{"className":1865,"style":619},[643],[573,1867,1868,1871],{"style":646},[573,1869],{"className":1870,"style":651},[650],[573,1872,1874],{"className":1873},[655,656,657,658],[573,1875,600],{"className":1876,"style":662},[623,627,658],[573,1878],{"className":1879,"style":1019},[705],[573,1881,937],{"className":1882},[1023],[573,1884],{"className":1885,"style":1019},[705],[573,1887,1889,1892,1895,1924],{"className":1888},[614],[573,1890],{"className":1891,"style":952},[618],[573,1893,921],{"className":1894},[956],[573,1896,1898,1901],{"className":1897},[623],[573,1899,597],{"className":1900},[623,627],[573,1902,1904],{"className":1903},[631],[573,1905,1907],{"className":1906},[635],[573,1908,1910],{"className":1909},[639],[573,1911,1913],{"className":1912,"style":619},[643],[573,1914,1915,1918],{"style":646},[573,1916],{"className":1917,"style":651},[650],[573,1919,1921],{"className":1920},[655,656,657,658],[573,1922,600],{"className":1923,"style":662},[623,627,658],[573,1925,1927,1930],{"className":1926},[989],[573,1928,932],{"className":1929},[989],[573,1931,1933],{"className":1932},[631],[573,1934,1936],{"className":1935},[635],[573,1937,1939],{"className":1938},[639],[573,1940,1942],{"className":1941,"style":1830},[643],[573,1943,1944,1947],{"style":646},[573,1945],{"className":1946,"style":651},[650],[573,1948,1950],{"className":1949},[655,656,657,658],[573,1951,1953,1956],{"className":1952},[623,658],[573,1954,1766],{"className":1955},[623,658],[573,1957,1770],{"className":1958},[623,658]," für invertierbare ",[573,1961,1963,1976],{"className":1962},[576],[573,1964,1966],{"className":1965},[580],[582,1967,1968],{"xmlns":584},[586,1969,1970,1974],{},[589,1971,1972],{},[595,1973,597],{},[602,1975,597],{"encoding":604},[573,1977,1979],{"className":1978,"ariaHidden":610},[609],[573,1980,1982,1985],{"className":1981},[614],[573,1983],{"className":1984,"style":1033},[618],[573,1986,597],{"className":1987},[623,627],[904,1989,1990,1239,2103,896],{},[573,1991,1993,2029],{"className":1992},[576],[573,1994,1996],{"className":1995},[580],[582,1997,1998],{"xmlns":584},[586,1999,2000,2026],{},[589,2001,2002,2005,2008,2010,2016,2018,2020,2022,2024],{},[595,2003,2004],{},"det",[680,2006,2007],{},"⁡",[680,2009,921],{"stretchy":920},[592,2011,2012,2014],{},[595,2013,597],{},[595,2015,600],{},[680,2017,932],{"stretchy":920},[680,2019,937],{},[595,2021,2004],{},[680,2023,2007],{},[595,2025,597],{},[602,2027,2028],{"encoding":604},"\\det(A^T) = \\det A",[573,2030,2032,2086],{"className":2031,"ariaHidden":610},[609],[573,2033,2035,2038,2042,2045,2074,2077,2080,2083],{"className":2034},[614],[573,2036],{"className":2037,"style":952},[618],[573,2039,2004],{"className":2040},[2041],"mop",[573,2043,921],{"className":2044},[956],[573,2046,2048,2051],{"className":2047},[623],[573,2049,597],{"className":2050},[623,627],[573,2052,2054],{"className":2053},[631],[573,2055,2057],{"className":2056},[635],[573,2058,2060],{"className":2059},[639],[573,2061,2063],{"className":2062,"style":619},[643],[573,2064,2065,2068],{"style":646},[573,2066],{"className":2067,"style":651},[650],[573,2069,2071],{"className":2070},[655,656,657,658],[573,2072,600],{"className":2073,"style":662},[623,627,658],[573,2075,932],{"className":2076},[989],[573,2078],{"className":2079,"style":1019},[705],[573,2081,937],{"className":2082},[1023],[573,2084],{"className":2085,"style":1019},[705],[573,2087,2089,2093,2096,2100],{"className":2088},[614],[573,2090],{"className":2091,"style":2092},[618],"height:0.6944em;",[573,2094,2004],{"className":2095},[2041],[573,2097],{"className":2098,"style":2099},[705],"margin-right:0.1667em;",[573,2101,597],{"className":2102},[623,627],[573,2104,2106,2146],{"className":2105},[576],[573,2107,2109],{"className":2108},[580],[582,2110,2111],{"xmlns":584},[586,2112,2113,2143],{},[589,2114,2115,2119,2121,2123,2129,2131,2133,2135,2137,2139,2141],{},[595,2116,2118],{"mathvariant":2117},"normal","rg",[680,2120,2007],{},[680,2122,921],{"stretchy":920},[592,2124,2125,2127],{},[595,2126,597],{},[595,2128,600],{},[680,2130,932],{"stretchy":920},[680,2132,937],{},[595,2134,2118],{"mathvariant":2117},[680,2136,2007],{},[680,2138,921],{"stretchy":920},[595,2140,597],{},[680,2142,932],{"stretchy":920},[602,2144,2145],{"encoding":604},"\\operatorname{rg}(A^T) = \\operatorname{rg}(A)",[573,2147,2149,2207],{"className":2148,"ariaHidden":610},[609],[573,2150,2152,2155,2163,2166,2195,2198,2201,2204],{"className":2151},[614],[573,2153],{"className":2154,"style":952},[618],[573,2156,2158],{"className":2157},[2041],[573,2159,2118],{"className":2160,"style":2162},[623,2161],"mathrm","margin-right:0.0139em;",[573,2164,921],{"className":2165},[956],[573,2167,2169,2172],{"className":2168},[623],[573,2170,597],{"className":2171},[623,627],[573,2173,2175],{"className":2174},[631],[573,2176,2178],{"className":2177},[635],[573,2179,2181],{"className":2180},[639],[573,2182,2184],{"className":2183,"style":619},[643],[573,2185,2186,2189],{"style":646},[573,2187],{"className":2188,"style":651},[650],[573,2190,2192],{"className":2191},[655,656,657,658],[573,2193,600],{"className":2194,"style":662},[623,627,658],[573,2196,932],{"className":2197},[989],[573,2199],{"className":2200,"style":1019},[705],[573,2202,937],{"className":2203},[1023],[573,2205],{"className":2206,"style":1019},[705],[573,2208,2210,2213,2219,2222,2225],{"className":2209},[614],[573,2211],{"className":2212,"style":1095},[618],[573,2214,2216],{"className":2215},[2041],[573,2217,2118],{"className":2218,"style":2162},[623,2161],[573,2220,921],{"className":2221},[956],[573,2223,597],{"className":2224},[623,627],[573,2226,932],{"className":2227},[989],[564,2229,2230,2231,1239,2334,2431,2432,2526,2527,1239,2580,2631],{},"Die Umkehr der Reihenfolge ist schon aus Größengründen nötig: Für ",[573,2232,2234,2267],{"className":2233},[576],[573,2235,2237],{"className":2236},[580],[582,2238,2239],{"xmlns":584},[586,2240,2241,2264],{},[589,2242,2243,2245,2248],{},[595,2244,597],{},[680,2246,2247],{},"∈",[592,2249,2250,2254],{},[595,2251,2253],{"mathvariant":2252},"double-struck","R",[589,2255,2256,2259,2261],{},[1768,2257,2258],{},"2",[680,2260,682],{},[1768,2262,2263],{},"3",[602,2265,2266],{"encoding":604},"A \\in \\mathbb{R}^{2 \\times 3}",[573,2268,2270,2289],{"className":2269,"ariaHidden":610},[609],[573,2271,2273,2277,2280,2283,2286],{"className":2272},[614],[573,2274],{"className":2275,"style":2276},[618],"height:0.7224em;vertical-align:-0.0391em;",[573,2278,597],{"className":2279},[623,627],[573,2281],{"className":2282,"style":1019},[705],[573,2284,2247],{"className":2285},[1023],[573,2287],{"className":2288,"style":1019},[705],[573,2290,2292,2295],{"className":2291},[614],[573,2293],{"className":2294,"style":1830},[618],[573,2296,2298,2302],{"className":2297},[623],[573,2299,2253],{"className":2300},[623,2301],"mathbb",[573,2303,2305],{"className":2304},[631],[573,2306,2308],{"className":2307},[635],[573,2309,2311],{"className":2310},[639],[573,2312,2314],{"className":2313,"style":1830},[643],[573,2315,2316,2319],{"style":646},[573,2317],{"className":2318,"style":651},[650],[573,2320,2322],{"className":2321},[655,656,657,658],[573,2323,2325,2328,2331],{"className":2324},[623,658],[573,2326,2258],{"className":2327},[623,658],[573,2329,682],{"className":2330},[710,658],[573,2332,2263],{"className":2333},[623,658],[573,2335,2337,2366],{"className":2336},[576],[573,2338,2340],{"className":2339},[580],[582,2341,2342],{"xmlns":584},[586,2343,2344,2363],{},[589,2345,2346,2348,2350],{},[595,2347,1392],{},[680,2349,2247],{},[592,2351,2352,2354],{},[595,2353,2253],{"mathvariant":2252},[589,2355,2356,2358,2360],{},[1768,2357,2263],{},[680,2359,682],{},[1768,2361,2362],{},"4",[602,2364,2365],{"encoding":604},"B \\in \\mathbb{R}^{3 \\times 4}",[573,2367,2369,2387],{"className":2368,"ariaHidden":610},[609],[573,2370,2372,2375,2378,2381,2384],{"className":2371},[614],[573,2373],{"className":2374,"style":2276},[618],[573,2376,1392],{"className":2377,"style":1433},[623,627],[573,2379],{"className":2380,"style":1019},[705],[573,2382,2247],{"className":2383},[1023],[573,2385],{"className":2386,"style":1019},[705],[573,2388,2390,2393],{"className":2389},[614],[573,2391],{"className":2392,"style":1830},[618],[573,2394,2396,2399],{"className":2395},[623],[573,2397,2253],{"className":2398},[623,2301],[573,2400,2402],{"className":2401},[631],[573,2403,2405],{"className":2404},[635],[573,2406,2408],{"className":2407},[639],[573,2409,2411],{"className":2410,"style":1830},[643],[573,2412,2413,2416],{"style":646},[573,2414],{"className":2415,"style":651},[650],[573,2417,2419],{"className":2418},[655,656,657,658],[573,2420,2422,2425,2428],{"className":2421},[623,658],[573,2423,2263],{"className":2424},[623,658],[573,2426,682],{"className":2427},[710,658],[573,2429,2362],{"className":2430},[623,658]," ist ",[573,2433,2435,2459],{"className":2434},[576],[573,2436,2438],{"className":2437},[580],[582,2439,2440],{"xmlns":584},[586,2441,2442,2456],{},[589,2443,2444,2450],{},[592,2445,2446,2448],{},[595,2447,597],{},[595,2449,600],{},[592,2451,2452,2454],{},[595,2453,1392],{},[595,2455,600],{},[602,2457,2458],{"encoding":604},"A^T B^T",[573,2460,2462],{"className":2461,"ariaHidden":610},[609],[573,2463,2465,2468,2497],{"className":2464},[614],[573,2466],{"className":2467,"style":619},[618],[573,2469,2471,2474],{"className":2470},[623],[573,2472,597],{"className":2473},[623,627],[573,2475,2477],{"className":2476},[631],[573,2478,2480],{"className":2479},[635],[573,2481,2483],{"className":2482},[639],[573,2484,2486],{"className":2485,"style":619},[643],[573,2487,2488,2491],{"style":646},[573,2489],{"className":2490,"style":651},[650],[573,2492,2494],{"className":2493},[655,656,657,658],[573,2495,600],{"className":2496,"style":662},[623,627,658],[573,2498,2500,2503],{"className":2499},[623],[573,2501,1392],{"className":2502,"style":1433},[623,627],[573,2504,2506],{"className":2505},[631],[573,2507,2509],{"className":2508},[635],[573,2510,2512],{"className":2511},[639],[573,2513,2515],{"className":2514,"style":619},[643],[573,2516,2517,2520],{"style":646},[573,2518],{"className":2519,"style":651},[650],[573,2521,2523],{"className":2522},[655,656,657,658],[573,2524,600],{"className":2525,"style":662},[623,627,658]," ein Produkt aus ",[573,2528,2530,2548],{"className":2529},[576],[573,2531,2533],{"className":2532},[580],[582,2534,2535],{"xmlns":584},[586,2536,2537,2545],{},[589,2538,2539,2541,2543],{},[1768,2540,2263],{},[680,2542,682],{},[1768,2544,2258],{},[602,2546,2547],{"encoding":604},"3 \\times 2",[573,2549,2551,2570],{"className":2550,"ariaHidden":610},[609],[573,2552,2554,2558,2561,2564,2567],{"className":2553},[614],[573,2555],{"className":2556,"style":2557},[618],"height:0.7278em;vertical-align:-0.0833em;",[573,2559,2263],{"className":2560},[623],[573,2562],{"className":2563,"style":706},[705],[573,2565,682],{"className":2566},[710],[573,2568],{"className":2569,"style":706},[705],[573,2571,2573,2577],{"className":2572},[614],[573,2574],{"className":2575,"style":2576},[618],"height:0.6444em;",[573,2578,2258],{"className":2579},[623],[573,2581,2583,2601],{"className":2582},[576],[573,2584,2586],{"className":2585},[580],[582,2587,2588],{"xmlns":584},[586,2589,2590,2598],{},[589,2591,2592,2594,2596],{},[1768,2593,2362],{},[680,2595,682],{},[1768,2597,2263],{},[602,2599,2600],{"encoding":604},"4 \\times 3",[573,2602,2604,2622],{"className":2603,"ariaHidden":610},[609],[573,2605,2607,2610,2613,2616,2619],{"className":2606},[614],[573,2608],{"className":2609,"style":2557},[618],[573,2611,2362],{"className":2612},[623],[573,2614],{"className":2615,"style":706},[705],[573,2617,682],{"className":2618},[710],[573,2620],{"className":2621,"style":706},[705],[573,2623,2625,2628],{"className":2624},[614],[573,2626],{"className":2627,"style":2576},[618],[573,2629,2263],{"className":2630},[623],", das gar nicht definiert ist.",[564,2633,2634,2635,2716,2717,2720,2721,2431,2749,2813,2814,3102,3103,3391],{},"Eine Matrix mit ",[573,2636,2638,2660],{"className":2637},[576],[573,2639,2641],{"className":2640},[580],[582,2642,2643],{"xmlns":584},[586,2644,2645,2657],{},[589,2646,2647,2653,2655],{},[592,2648,2649,2651],{},[595,2650,597],{},[595,2652,600],{},[680,2654,937],{},[595,2656,597],{},[602,2658,2659],{"encoding":604},"A^T = A",[573,2661,2663,2707],{"className":2662,"ariaHidden":610},[609],[573,2664,2666,2669,2698,2701,2704],{"className":2665},[614],[573,2667],{"className":2668,"style":619},[618],[573,2670,2672,2675],{"className":2671},[623],[573,2673,597],{"className":2674},[623,627],[573,2676,2678],{"className":2677},[631],[573,2679,2681],{"className":2680},[635],[573,2682,2684],{"className":2683},[639],[573,2685,2687],{"className":2686,"style":619},[643],[573,2688,2689,2692],{"style":646},[573,2690],{"className":2691,"style":651},[650],[573,2693,2695],{"className":2694},[655,656,657,658],[573,2696,600],{"className":2697,"style":662},[623,627,658],[573,2699],{"className":2700,"style":1019},[705],[573,2702,937],{"className":2703},[1023],[573,2705],{"className":2706,"style":1019},[705],[573,2708,2710,2713],{"className":2709},[614],[573,2711],{"className":2712,"style":1033},[618],[573,2714,597],{"className":2715},[623,627]," heißt ",[568,2718,2719],{},"symmetrisch",". Für jede Matrix ",[573,2722,2724,2737],{"className":2723},[576],[573,2725,2727],{"className":2726},[580],[582,2728,2729],{"xmlns":584},[586,2730,2731,2735],{},[589,2732,2733],{},[595,2734,597],{},[602,2736,597],{"encoding":604},[573,2738,2740],{"className":2739,"ariaHidden":610},[609],[573,2741,2743,2746],{"className":2742},[614],[573,2744],{"className":2745,"style":1033},[618],[573,2747,597],{"className":2748},[623,627],[573,2750,2752,2772],{"className":2751},[576],[573,2753,2755],{"className":2754},[580],[582,2756,2757],{"xmlns":584},[586,2758,2759,2769],{},[589,2760,2761,2767],{},[592,2762,2763,2765],{},[595,2764,597],{},[595,2766,600],{},[595,2768,597],{},[602,2770,2771],{"encoding":604},"A^T A",[573,2773,2775],{"className":2774,"ariaHidden":610},[609],[573,2776,2778,2781,2810],{"className":2777},[614],[573,2779],{"className":2780,"style":619},[618],[573,2782,2784,2787],{"className":2783},[623],[573,2785,597],{"className":2786},[623,627],[573,2788,2790],{"className":2789},[631],[573,2791,2793],{"className":2792},[635],[573,2794,2796],{"className":2795},[639],[573,2797,2799],{"className":2798,"style":619},[643],[573,2800,2801,2804],{"style":646},[573,2802],{"className":2803,"style":651},[650],[573,2805,2807],{"className":2806},[655,656,657,658],[573,2808,600],{"className":2809,"style":662},[623,627,658],[573,2811,597],{"className":2812},[623,627]," symmetrisch, denn ",[573,2815,2817,2877],{"className":2816},[576],[573,2818,2820],{"className":2819},[580],[582,2821,2822],{"xmlns":584},[586,2823,2824,2874],{},[589,2825,2826,2828,2834,2836,2842,2844,2850,2852,2858,2864,2866,2872],{},[680,2827,921],{"stretchy":920},[592,2829,2830,2832],{},[595,2831,597],{},[595,2833,600],{},[595,2835,597],{},[592,2837,2838,2840],{},[680,2839,932],{"stretchy":920},[595,2841,600],{},[680,2843,937],{},[592,2845,2846,2848],{},[595,2847,597],{},[595,2849,600],{},[680,2851,921],{"stretchy":920},[592,2853,2854,2856],{},[595,2855,597],{},[595,2857,600],{},[592,2859,2860,2862],{},[680,2861,932],{"stretchy":920},[595,2863,600],{},[680,2865,937],{},[592,2867,2868,2870],{},[595,2869,597],{},[595,2871,600],{},[595,2873,597],{},[602,2875,2876],{"encoding":604},"(A^T A)^T = A^T (A^T)^T = A^T 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Das Standardskalarprodukt lässt sich als ",[573,3104,3106,3161],{"className":3105},[576],[573,3107,3109],{"className":3108},[580],[582,3110,3111],{"xmlns":584},[586,3112,3113,3158],{},[589,3114,3115,3124,3127,3134,3136,3152],{},[3116,3117,3118,3121],"mover",{"accent":610},[595,3119,3120],{},"u",[680,3122,3123],{},"⃗",[680,3125,3126],{},"⋅",[3116,3128,3129,3132],{"accent":610},[595,3130,3131],{},"v",[680,3133,3123],{},[680,3135,937],{},[592,3137,3138,3144],{},[3116,3139,3140,3142],{"accent":610},[595,3141,3120],{},[680,3143,3123],{},[589,3145,3146,3150],{},[3147,3148,3149],"mtext",{}," ",[595,3151,600],{},[3116,3153,3154,3156],{"accent":610},[595,3155,3131],{},[680,3157,3123],{},[602,3159,3160],{"encoding":604},"\\vec u \\cdot \\vec v = \\vec u^{\\,T} \\vec 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= \\begin{pmatrix} 2 & 1 \\\\ 4 & 3 \\end{pmatrix}, \\qquad (AB)^T = \\begin{pmatrix} 2 & 4 \\\\ 1 & 3 \\end{pmatrix} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix} \\begin{pmatrix} 1 & 3 \\\\ 2 & 4 \\end{pmatrix} = B^T A^T.",[573,4030,4032,4053,4239,4371,4623],{"className":4031,"ariaHidden":610},[609],[573,4033,4035,4038,4041,4044,4047,4050],{"className":4034},[614],[573,4036],{"className":4037,"style":1033},[618],[573,4039,597],{"className":4040},[623,627],[573,4042,1392],{"className":4043,"style":1433},[623,627],[573,4045],{"className":4046,"style":1019},[705],[573,4048,937],{"className":4049},[1023],[573,4051],{"className":4052,"style":1019},[705],[573,4054,4056,4059,4176,4179,4183,4187,4190,4193,4196,4199,4230,4233,4236],{"className":4055},[614],[573,4057],{"className":4058,"style":3489},[618],[573,4060,4062,4068,4170],{"className":4061},[3493],[573,4063,4065],{"className":4064,"style":3498},[956,3497],[573,4066,921],{"className":4067},[3502,657],[573,4069,4071],{"className":4070},[623],[573,4072,4074,4119,4122,4125],{"className":4073},[3420],[573,4075,4077],{"className":4076},[3512],[573,4078,4080,4111],{"className":4079},[635,3516],[573,4081,4083,4108],{"className":4082},[639],[573,4084,4086,4097],{"className":4085,"style":3523},[643],[573,4087,4088,4091],{"style":3526},[573,4089],{"className":4090,"style":3190},[650],[573,4092,4094],{"className":4093},[623],[573,4095,2258],{"className":4096},[623],[573,4098,4099,4102],{"style":3538},[573,4100],{"className":4101,"style":3190},[650],[573,4103,4105],{"className":4104},[623],[573,4106,2362],{"className":4107},[623],[573,4109,3552],{"className":4110},[3551],[573,4112,4114],{"className":4113},[639],[573,4115,4117],{"className":4116,"style":3559},[643],[573,4118],{},[573,4120],{"className":4121,"style":3566},[3565],[573,4123],{"className":4124,"style":3566},[3565],[573,4126,4128],{"className":4127},[3512],[573,4129,4131,4162],{"className":4130},[635,3516],[573,4132,4134,4159],{"className":4133},[639],[573,4135,4137,4148],{"className":4136,"style":3523},[643],[573,4138,4139,4142],{"style":3526},[573,4140],{"className":4141,"style":3190},[650],[573,4143,4145],{"className":4144},[623],[573,4146,1770],{"className":4147},[623],[573,4149,4150,4153],{"style":3538},[573,4151],{"className":4152,"style":3190},[650],[573,4154,4156],{"className":4155},[623],[573,4157,2263],{"className":4158},[623],[573,4160,3552],{"className":4161},[3551],[573,4163,4165],{"className":4164},[639],[573,4166,4168],{"className":4167,"style":3559},[643],[573,4169],{},[573,4171,4173],{"className":4172,"style":3498},[989,3497],[573,4174,932],{"className":4175},[3502,657],[573,4177],{"className":4178,"style":2099},[705],[573,4180,3882],{"className":4181},[4182],"mpunct",[573,4184],{"className":4185,"style":4186},[705],"margin-right:2em;",[573,4188],{"className":4189,"style":2099},[705],[573,4191,921],{"className":4192},[956],[573,4194,597],{"className":4195},[623,627],[573,4197,1392],{"className":4198,"style":1433},[623,627],[573,4200,4202,4205],{"className":4201},[989],[573,4203,932],{"className":4204},[989],[573,4206,4208],{"className":4207},[631],[573,4209,4211],{"className":4210},[635],[573,4212,4214],{"className":4213},[639],[573,4215,4218],{"className":4216,"style":4217},[643],"height:0.8913em;",[573,4219,4221,4224],{"style":4220},"top:-3.113em;margin-right:0.05em;",[573,4222],{"className":4223,"style":651},[650],[573,4225,4227],{"className":4226},[655,656,657,658],[573,4228,600],{"className":4229,"style":662},[623,627,658],[573,4231],{"className":4232,"style":1019},[705],[573,4234,937],{"className":4235},[1023],[573,4237],{"className":4238,"style":1019},[705],[573,4240,4242,4245,4362,4365,4368],{"className":4241},[614],[573,4243],{"className":4244,"style":3489},[618],[573,4246,4248,4254,4356],{"className":4247},[3493],[573,4249,4251],{"className":4250,"style":3498},[956,3497],[573,4252,921],{"className":4253},[3502,657],[573,4255,4257],{"className":4256},[623],[573,4258,4260,4305,4308,4311],{"className":4259},[3420],[573,4261,4263],{"className":4262},[3512],[573,4264,4266,4297],{"className":4265},[635,3516],[573,4267,4269,4294],{"className":4268},[639],[573,4270,4272,4283],{"className":4271,"style":3523},[643],[573,4273,4274,4277],{"style":3526},[573,4275],{"className":4276,"style":3190},[650],[573,4278,4280],{"className":4279},[623],[573,4281,2258],{"className":4282},[623],[573,4284,4285,4288],{"style":3538},[573,4286],{"className":4287,"style":3190},[650],[573,4289,4291],{"className":4290},[623],[573,4292,1770],{"className":4293},[623],[573,4295,3552],{"className":4296},[3551],[573,4298,4300],{"className":4299},[639],[573,4301,4303],{"className":4302,"style":3559},[643],[573,4304],{},[573,4306],{"className":4307,"style":3566},[3565],[573,4309],{"className":4310,"style":3566},[3565],[573,4312,4314],{"className":4313},[3512],[573,4315,4317,4348],{"className":4316},[635,3516],[573,4318,4320,4345],{"className":4319},[639],[573,4321,4323,4334],{"className":4322,"style":3523},[643],[573,4324,4325,4328],{"style":3526},[573,4326],{"className":4327,"style":3190},[650],[573,4329,4331],{"className":4330},[623],[573,4332,2362],{"className":4333},[623],[573,4335,4336,4339],{"style":3538},[573,4337],{"className":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ssName":4657,"style":662},[623,627,658],[573,4659,4661,4664],{"className":4660},[623],[573,4662,597],{"className":4663},[623,627],[573,4665,4667],{"className":4666},[631],[573,4668,4670],{"className":4669},[635],[573,4671,4673],{"className":4672},[639],[573,4674,4676],{"className":4675,"style":4217},[643],[573,4677,4678,4681],{"style":4220},[573,4679],{"className":4680,"style":651},[650],[573,4682,4684],{"className":4683},[655,656,657,658],[573,4685,600],{"className":4686,"style":662},[623,627,658],[573,4688,896],{"className":4689},[623],[564,4691,4692,4693,4957],{},"Die falsche Reihenfolge liefert ",[573,4694,4696,4758],{"className":4695},[576],[573,4697,4699],{"className":4698},[580],[582,4700,4701],{"xmlns":584},[586,4702,4703,4755],{},[589,4704,4705,4711,4717,4719],{},[592,4706,4707,4709],{},[595,4708,597],{},[595,4710,600],{},[592,4712,4713,4715],{},[595,4714,1392],{},[595,4716,600],{},[680,4718,937],{},[589,4720,4721,4723,4753],{},[680,4722,921],{"fence":610},[3420,4724,4725,4739],{"rowspacing":3422,"columnalign":3423,"columnspacing":3424},[3426,4726,4727,4733],{},[3429,4728,4729],{},[3432,4730,4731],{"scriptlevel":3434,"displaystyle":920},[1768,4732,2263],{},[3429,4734,4735],{},[3432,4736,4737],{"scriptlevel":3434,"displaystyle":920},[1768,4738,1770],{},[3426,4740,4741,4747],{},[3429,4742,4743],{},[3432,4744,4745],{"scriptlevel":3434,"displaystyle":920},[1768,4746,2362],{},[3429,4748,4749],{},[3432,4750,4751],{"scriptlevel":3434,"displaystyle":920},[1768,4752,2258],{},[680,4754,932],{"fence":610},[602,4756,4757],{"encoding":604},"A^T B^T = \\begin{pmatrix} 3 & 1 \\\\ 4 & 2 \\end{pmatrix}",[573,4759,4761,4834],{"className":4760,"ariaHidden":610},[609],[573,4762,4764,4767,4796,4825,4828,4831],{"className":4763},[614],[573,4765],{"className":4766,"style":619},[618],[573,4768,4770,4773],{"className":4769},[623],[573,4771,597],{"className":4772},[623,627],[573,4774,4776],{"className":4775},[631],[573,4777,4779],{"className":4778},[635],[573,4780,4782],{"className":4781},[639],[573,4783,4785],{"className":4784,"style":619},[643],[573,4786,4787,4790],{"style":646},[573,4788],{"className":4789,"style":651},[650],[573,4791,4793],{"className":4792},[655,656,657,658],[573,4794,600],{"className":4795,"style":662},[623,627,658],[573,4797,4799,4802],{"className":4798},[623],[573,4800,1392],{"className":4801,"style":1433},[623,627],[573,4803,4805],{"className":4804},[631],[573,4806,4808],{"className":4807},[635],[573,4809,4811],{"className":4810},[639],[573,4812,4814],{"className":4813,"style":619},[643],[573,4815,4816,4819],{"style":646},[573,4817],{"className":4818,"style":651},[650],[573,4820,4822],{"className":4821},[655,656,657,658],[573,4823,600],{"className":4824,"style":662},[623,627,658],[573,4826],{"className":4827,"style":1019},[705],[573,4829,937],{"className":4830},[1023],[573,4832],{"className":4833,"style":1019},[705],[573,4835,4837,4840],{"className":4836},[614],[573,4838],{"className":4839,"style":3489},[618],[573,4841,4843,4849,4951],{"className":4842},[3493],[573,4844,4846],{"className":4845,"style":3498},[956,3497],[573,4847,921],{"className":4848},[3502,657],[573,4850,4852],{"className":4851},[623],[573,4853,4855,4900,4903,4906],{"className":4854},[3420],[573,4856,4858],{"className":4857},[3512],[573,4859,4861,4892],{"className":4860},[635,3516],[573,4862,4864,4889],{"className":4863},[639],[573,4865,4867,4878],{"className":4866,"style":3523},[643],[573,4868,4869,4872],{"style":3526},[573,4870],{"className":4871,"style":3190},[650],[573,4873,4875],{"className":4874},[623],[573,4876,2263],{"className":4877},[623],[573,4879,4880,4883],{"style":3538},[573,4881],{"className":4882,"style":3190},[650],[573,4884,4886],{"className":4885},[623],[573,4887,2362],{"className":4888},[623],[573,4890,3552],{"className":4891},[3551],[573,4893,4895],{"className":4894},[639],[573,4896,4898],{"className":4897,"style":3559},[643],[573,4899],{},[573,4901],{"className":4902,"style":3566},[3565],[573,4904],{"className":4905,"style":3566},[3565],[573,4907,4909],{"className":4908},[3512],[573,4910,4912,4943],{"className":4911},[635,3516],[573,4913,4915,4940],{"className":4914},[639],[573,4916,4918,4929],{"className":4917,"style":3523},[643],[573,4919,4920,4923],{"style":3526},[573,4921],{"className":4922,"style":3190},[650],[573,4924,4926],{"className":4925},[623],[573,4927,1770],{"className":4928},[623],[573,4930,4931,4934],{"style":3538},[573,4932],{"className":4933,"style":3190},[650],[573,4935,4937],{"className":4936},[623],[573,4938,2258],{"className":4939},[623],[573,4941,3552],{"className":4942},[3551],[573,4944,4946],{"className":4945},[639],[573,4947,4949],{"className":4948,"style":3559},[643],[573,4950],{},[573,4952,4954],{"className":4953,"style":3498},[989,3497],[573,4955,932],{"className":4956},[3502,657],", eine andere Matrix.",[564,4959,4960,4961,1239,5125,2431,5288,5524,5525,5576],{},"Mit ",[573,4962,4964,5007],{"className":4963},[576],[573,4965,4967],{"className":4966},[580],[582,4968,4969],{"xmlns":584},[586,4970,4971,5004],{},[589,4972,4973,4979,4981,4983,4985,4987,4990,4992,4994,4996,4998],{},[3116,4974,4975,4977],{"accent":610},[595,4976,3120],{},[680,4978,3123],{},[680,4980,937],{},[680,4982,921],{"stretchy":920},[1768,4984,1770],{},[680,4986,3882],{"separator":610},[3147,4988,4989],{}," ",[1768,4991,2258],{},[680,4993,3882],{"separator":610},[3147,4995,4989],{},[1768,4997,2258],{},[592,4999,5000,5002],{},[680,5001,932],{"stretchy":920},[595,5003,600],{},[602,5005,5006],{"encoding":604},"\\vec u = (1,\\ 2,\\ 2)^T",[573,5008,5010,5060],{"className":5009,"ariaHidden":610},[609],[573,5011,5013,5016,5051,5054,5057],{"className":5012},[614],[573,5014],{"className":5015,"style":3170},[618],[573,5017,5019],{"className":5018},[623,3174],[573,5020,5022],{"className":5021},[635],[573,5023,5025],{"className":5024},[639],[573,5026,5028,5036],{"className":5027,"style":3170},[643],[573,5029,5030,5033],{"style":3186},[573,5031],{"className":5032,"style":3190},[650],[573,5034,3120],{"className":5035},[623,627],[573,5037,5038,5041],{"style":3186},[573,5039],{"className":5040,"style":3190},[650],[573,5042,5044],{"className":5043,"style":3203},[3202],[573,5045,5047],{"className":5046,"style":3208},[3207],[3210,5048,5049],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,5050],{"d":3221},[573,5052],{"className":5053,"style":1019},[705],[573,5055,937],{"className":5056},[1023],[573,5058],{"className":5059,"style":1019},[705],[573,5061,5063,5066,5069,5072,5075,5078,5081,5084,5087,5090,5093,5096],{"className":5062},[614],[573,5064],{"className":5065,"style":952},[618],[573,5067,921],{"className":5068},[956],[573,5070,1770],{"className":5071},[623],[573,5073,3882],{"className":5074},[4182],[573,5076,4989],{"className":5077},[705],[573,5079],{"className":5080,"style":2099},[705],[573,5082,2258],{"className":5083},[623],[573,5085,3882],{"className":5086},[4182],[573,5088,4989],{"className":5089},[705],[573,5091],{"className":5092,"style":2099},[705],[573,5094,2258],{"className":5095},[623],[573,5097,5099,5102],{"className":5098},[989],[573,5100,932],{"className":5101},[989],[573,5103,5105],{"className":5104},[631],[573,5106,5108],{"className":5107},[635],[573,5109,5111],{"className":5110},[639],[573,5112,5114],{"className":5113,"style":619},[643],[573,5115,5116,5119],{"style":646},[573,5117],{"className":5118,"style":651},[650],[573,5120,5122],{"className":5121},[655,656,657,658],[573,5123,600],{"className":5124,"style":662},[623,627,658],[573,5126,5128,5170],{"className":5127},[576],[573,5129,5131],{"className":5130},[580],[582,5132,5133],{"xmlns":584},[586,5134,5135,5167],{},[589,5136,5137,5143,5145,5147,5149,5151,5153,5155,5157,5159,5161],{},[3116,5138,5139,5141],{"accent":610},[595,5140,3131],{},[680,5142,3123],{},[680,5144,937],{},[680,5146,921],{"stretchy":920},[1768,5148,2263],{},[680,5150,3882],{"separator":610},[3147,5152,4989],{},[1768,5154,3434],{},[680,5156,3882],{"separator":610},[3147,5158,4989],{},[1768,5160,2362],{},[592,5162,5163,5165],{},[680,5164,932],{"stretchy":920},[595,5166,600],{},[602,5168,5169],{"encoding":604},"\\vec v = (3,\\ 0,\\ 4)^T",[573,5171,5173,5223],{"className":5172,"ariaHidden":610},[609],[573,5174,5176,5179,5214,5217,5220],{"className":5175},[614],[573,5177],{"className":5178,"style":3170},[618],[573,5180,5182],{"className":5181},[623,3174],[573,5183,5185],{"className":5184},[635],[573,5186,5188],{"className":5187},[639],[573,5189,5191,5199],{"className":5190,"style":3170},[643],[573,5192,5193,5196],{"style":3186},[573,5194],{"className":5195,"style":3190},[650],[573,5197,3131],{"className":5198,"style":3257},[623,627],[573,5200,5201,5204],{"style":3186},[573,5202],{"className":5203,"style":3190},[650],[573,5205,5207],{"className":5206,"style":3203},[3202],[573,5208,5210],{"className":5209,"style":3208},[3207],[3210,5211,5212],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,5213],{"d":3221},[573,5215],{"className":5216,"style":1019},[705],[573,5218,937],{"className":5219},[1023],[573,5221],{"className":5222,"style":1019},[705],[573,5224,5226,5229,5232,5235,5238,5241,5244,5247,5250,5253,5256,5259],{"className":5225},[614],[573,5227],{"className":5228,"style":952},[618],[573,5230,921],{"className":5231},[956],[573,5233,2263],{"className":5234},[623],[573,5236,3882],{"className":5237},[4182],[573,5239,4989],{"className":5240},[705],[573,5242],{"className":5243,"style":2099},[705],[573,5245,3434],{"className":5246},[623],[573,5248,3882],{"className":5249},[4182],[573,5251,4989],{"className":5252},[705],[573,5254],{"className":5255,"style":2099},[705],[573,5257,2362],{"className":5258},[623],[573,5260,5262,5265],{"className":5261},[989],[573,5263,932],{"className":5264},[989],[573,5266,5268],{"className":5267},[631],[573,5269,5271],{"className":5270},[635],[573,5272,5274],{"className":5273},[639],[573,5275,5277],{"className":5276,"style":619},[643],[573,5278,5279,5282],{"style":646},[573,5280],{"className":5281,"style":651},[650],[573,5283,5285],{"className":5284},[655,656,657,658],[573,5286,600],{"className":5287,"style":662},[623,627,658],[573,5289,5291,5341],{"className":5290},[576],[573,5292,5294],{"className":5293},[580],[582,5295,5296],{"xmlns":584},[586,5297,5298,5338],{},[589,5299,5300,5314,5320,5322,5324,5326,5328,5330,5333,5335],{},[592,5301,5302,5308],{},[3116,5303,5304,5306],{"accent":610},[595,5305,3120],{},[680,5307,3123],{},[589,5309,5310,5312],{},[3147,5311,3149],{},[595,5313,600],{},[3116,5315,5316,5318],{"accent":610},[595,5317,3131],{},[680,5319,3123],{},[680,5321,937],{},[1768,5323,2263],{},[680,5325,1057],{},[1768,5327,3434],{},[680,5329,1057],{},[1768,5331,5332],{},"8",[680,5334,937],{},[1768,5336,5337],{},"11",[602,5339,5340],{"encoding":604},"\\vec u^{\\,T} \\vec v = 3 + 0 + 8 = 11",[573,5342,5344,5461,5479,5497,5515],{"className":5343,"ariaHidden":610},[609],[573,5345,5347,5350,5417,5452,5455,5458],{"className":5346},[614],[573,5348],{"className":5349,"style":619},[618],[573,5351,5353,5388],{"className":5352},[623],[573,5354,5356],{"className":5355},[623,3174],[573,5357,5359],{"className":5358},[635],[573,5360,5362],{"className":5361},[639],[573,5363,5365,5373],{"className":5364,"style":3170},[643],[573,5366,5367,5370],{"style":3186},[573,5368],{"className":5369,"style":3190},[650],[573,5371,3120],{"className":5372},[623,627],[573,5374,5375,5378],{"style":3186},[573,5376],{"className":5377,"style":3190},[650],[573,5379,5381],{"className":5380,"style":3203},[3202],[573,5382,5384],{"className":5383,"style":3208},[3207],[3210,5385,5386],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,5387],{"d":3221},[573,5389,5391],{"className":5390},[631],[573,5392,5394],{"className":5393},[635],[573,5395,5397],{"className":5396},[639],[573,5398,5400],{"className":5399,"style":619},[643],[573,5401,5402,5405],{"style":646},[573,5403],{"className":5404,"style":651},[650],[573,5406,5408],{"className":5407},[655,656,657,658],[573,5409,5411,5414],{"className":5410},[623,658],[573,5412],{"className":5413,"style":3352},[705,658],[573,5415,600],{"className":5416,"style":662},[623,627,658],[573,5418,5420],{"className":5419},[623,3174],[573,5421,5423],{"className":5422},[635],[573,5424,5426],{"className":5425},[639],[573,5427,5429,5437],{"className":5428,"style":3170},[643],[573,5430,5431,5434],{"style":3186},[573,5432],{"className":5433,"style":3190},[650],[573,5435,3131],{"className":5436,"style":3257},[623,627],[573,5438,5439,5442],{"style":3186},[573,5440],{"className":5441,"style":3190},[650],[573,5443,5445],{"className":5444,"style":3203},[3202],[573,5446,5448],{"className":5447,"style":3208},[3207],[3210,5449,5450],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,5451],{"d":3221},[573,5453],{"className":5454,"style":1019},[705],[573,5456,937],{"className":5457},[1023],[573,5459],{"className":5460,"style":1019},[705],[573,5462,5464,5467,5470,5473,5476],{"className":5463},[614],[573,5465],{"className":5466,"style":2557},[618],[573,5468,2263],{"className":5469},[623],[573,5471],{"className":5472,"style":706},[705],[573,5474,1057],{"className":5475},[710],[573,5477],{"className":5478,"style":706},[705],[573,5480,5482,5485,5488,5491,5494],{"className":5481},[614],[573,5483],{"className":5484,"style":2557},[618],[573,5486,3434],{"className":5487},[623],[573,5489],{"className":5490,"style":706},[705],[573,5492,1057],{"className":5493},[710],[573,5495],{"className":5496,"style":706},[705],[573,5498,5500,5503,5506,5509,5512],{"className":5499},[614],[573,5501],{"className":5502,"style":2576},[618],[573,5504,5332],{"className":5505},[623],[573,5507],{"className":5508,"style":1019},[705],[573,5510,937],{"className":5511},[1023],[573,5513],{"className":5514,"style":1019},[705],[573,5516,5518,5521],{"className":5517},[614],[573,5519],{"className":5520,"style":2576},[618],[573,5522,5337],{"className":5523},[623],", eine ",[573,5526,5528,5546],{"className":5527},[576],[573,5529,5531],{"className":5530},[580],[582,5532,5533],{"xmlns":584},[586,5534,5535,5543],{},[589,5536,5537,5539,5541],{},[1768,5538,1770],{},[680,5540,682],{},[1768,5542,1770],{},[602,5544,5545],{"encoding":604},"1 \\times 1",[573,5547,5549,5567],{"className":5548,"ariaHidden":610},[609],[573,5550,5552,5555,5558,5561,5564],{"className":5551},[614],[573,5553],{"className":5554,"style":2557},[618],[573,5556,1770],{"className":5557},[623],[573,5559],{"className":5560,"style":706},[705],[573,5562,682],{"className":5563},[710],[573,5565],{"className":5566,"style":706},[705],[573,5568,5570,5573],{"className":5569},[614],[573,5571],{"className":5572,"style":2576},[618],[573,5574,1770],{"className":5575},[623],"-Matrix, also eine Zahl.",[559,5578,5580],{"id":5579},"typische-fehler","Typische Fehler",[901,5582,5583,5841,5947],{},[904,5584,5585,5746,5747,896],{},[573,5586,5588,5626],{"className":5587},[576],[573,5589,5591],{"className":5590},[580],[582,5592,5593],{"xmlns":584},[586,5594,5595,5623],{},[589,5596,5597,5599,5601,5603,5609,5611,5617],{},[680,5598,921],{"stretchy":920},[595,5600,597],{},[595,5602,1392],{},[592,5604,5605,5607],{},[680,5606,932],{"stretchy":920},[595,5608,600],{},[680,5610,937],{},[592,5612,5613,5615],{},[595,5614,597],{},[595,5616,600],{},[592,5618,5619,5621],{},[595,5620,1392],{},[595,5622,600],{},[602,5624,5625],{"encoding":604},"(AB)^T = A^T B^T",[573,5627,5629,5682],{"className":5628,"ariaHidden":610},[609],[573,5630,5632,5635,5638,5641,5644,5673,5676,5679],{"className":5631},[614],[573,5633],{"className":5634,"style":952},[618],[573,5636,921],{"className":5637},[956],[573,5639,597],{"className":5640},[623,627],[573,5642,1392],{"className":5643,"style":1433},[623,627],[573,5645,5647,5650],{"className":5646},[989],[573,5648,932],{"className":5649},[989],[573,5651,5653],{"className":5652},[631],[573,5654,5656],{"className":5655},[635],[573,5657,5659],{"className":5658},[639],[573,5660,5662],{"className":5661,"style":619},[643],[573,5663,5664,5667],{"style":646},[573,5665],{"className":5666,"style":651},[650],[573,5668,5670],{"className":5669},[655,656,657,658],[573,5671,600],{"className":5672,"style":662},[623,627,658],[573,5674],{"className":5675,"style":1019},[705],[573,5677,937],{"className":5678},[1023],[573,5680],{"className":5681,"style":1019},[705],[573,5683,5685,5688,5717],{"className":5684},[614],[573,5686],{"className":5687,"style":619},[618],[573,5689,5691,5694],{"className":5690},[623],[573,5692,597],{"className":5693},[623,627],[573,5695,5697],{"className":5696},[631],[573,5698,5700],{"className":5699},[635],[573,5701,5703],{"className":5702},[639],[573,5704,5706],{"className":5705,"style":619},[643],[573,5707,5708,5711],{"style":646},[573,5709],{"className":5710,"style":651},[650],[573,5712,5714],{"className":5713},[655,656,657,658],[573,5715,600],{"className":5716,"style":662},[623,627,658],[573,5718,5720,5723],{"className":5719},[623],[573,5721,1392],{"className":5722,"style":1433},[623,627],[573,5724,5726],{"className":5725},[631],[573,5727,5729],{"className":5728},[635],[573,5730,5732],{"className":5731},[639],[573,5733,5735],{"className":5734,"style":619},[643],[573,5736,5737,5740],{"style":646},[573,5738],{"className":5739,"style":651},[650],[573,5741,5743],{"className":5742},[655,656,657,658],[573,5744,600],{"className":5745,"style":662},[623,627,658]," schreiben. Richtig ist ",[573,5748,5750,5774],{"className":5749},[576],[573,5751,5753],{"className":5752},[580],[582,5754,5755],{"xmlns":584},[586,5756,5757,5771],{},[589,5758,5759,5765],{},[592,5760,5761,5763],{},[595,5762,1392],{},[595,5764,600],{},[592,5766,5767,5769],{},[595,5768,597],{},[595,5770,600],{},[602,5772,5773],{"encoding":604},"B^T A^T",[573,5775,5777],{"className":5776,"ariaHidden":610},[609],[573,5778,5780,5783,5812],{"className":5779},[614],[573,5781],{"className":5782,"style":619},[618],[573,5784,5786,5789],{"className":5785},[623],[573,5787,1392],{"className":5788,"style":1433},[623,627],[573,5790,5792],{"className":5791},[631],[573,5793,5795],{"className":5794},[635],[573,5796,5798],{"className":5797},[639],[573,5799,5801],{"className":5800,"style":619},[643],[573,5802,5803,5806],{"style":646},[573,5804],{"className":5805,"style":651},[650],[573,5807,5809],{"className":5808},[655,656,657,658],[573,5810,600],{"className":5811,"style":662},[623,627,658],[573,5813,5815,5818],{"className":5814},[623],[573,5816,597],{"className":5817},[623,627],[573,5819,5821],{"className":5820},[631],[573,5822,5824],{"className":5823},[635],[573,5825,5827],{"className":5826},[639],[573,5828,5830],{"className":5829,"style":619},[643],[573,5831,5832,5835],{"style":646},[573,5833],{"className":5834,"style":651},[650],[573,5836,5838],{"className":5837},[655,656,657,658],[573,5839,600],{"className":5840,"style":662},[623,627,658],[904,5842,5843,5844,5895,5896,5946],{},"Beim Transponieren nur die Diagonale spiegeln und die Größe nicht anpassen. Eine ",[573,5845,5847,5865],{"className":5846},[576],[573,5848,5850],{"className":5849},[580],[582,5851,5852],{"xmlns":584},[586,5853,5854,5862],{},[589,5855,5856,5858,5860],{},[1768,5857,2258],{},[680,5859,682],{},[1768,5861,2263],{},[602,5863,5864],{"encoding":604},"2 \\times 3",[573,5866,5868,5886],{"className":5867,"ariaHidden":610},[609],[573,5869,5871,5874,5877,5880,5883],{"className":5870},[614],[573,5872],{"className":5873,"style":2557},[618],[573,5875,2258],{"className":5876},[623],[573,5878],{"className":5879,"style":706},[705],[573,5881,682],{"className":5882},[710],[573,5884],{"className":5885,"style":706},[705],[573,5887,5889,5892],{"className":5888},[614],[573,5890],{"className":5891,"style":2576},[618],[573,5893,2263],{"className":5894},[623],"-Matrix wird zur ",[573,5897,5899,5916],{"className":5898},[576],[573,5900,5902],{"className":5901},[580],[582,5903,5904],{"xmlns":584},[586,5905,5906,5914],{},[589,5907,5908,5910,5912],{},[1768,5909,2263],{},[680,5911,682],{},[1768,5913,2258],{},[602,5915,2547],{"encoding":604},[573,5917,5919,5937],{"className":5918,"ariaHidden":610},[609],[573,5920,5922,5925,5928,5931,5934],{"className":5921},[614],[573,5923],{"className":5924,"style":2557},[618],[573,5926,2263],{"className":5927},[623],[573,5929],{"className":5930,"style":706},[705],[573,5932,682],{"className":5933},[710],[573,5935],{"className":5936,"style":706},[705],[573,5938,5940,5943],{"className":5939},[614],[573,5941],{"className":5942,"style":2576},[618],[573,5944,2258],{"className":5945},[623],"-Matrix.",[904,5948,5949,6095,6096,6247,6248,6299],{},[573,5950,5952,5984],{"className":5951},[576],[573,5953,5955],{"className":5954},[580],[582,5956,5957],{"xmlns":584},[586,5958,5959,5981],{},[589,5960,5961,5975],{},[592,5962,5963,5969],{},[3116,5964,5965,5967],{"accent":610},[595,5966,3120],{},[680,5968,3123],{},[589,5970,5971,5973],{},[3147,5972,3149],{},[595,5974,600],{},[3116,5976,5977,5979],{"accent":610},[595,5978,3131],{},[680,5980,3123],{},[602,5982,5983],{"encoding":604},"\\vec u^{\\,T} \\vec v",[573,5985,5987],{"className":5986,"ariaHidden":610},[609],[573,5988,5990,5993,6060],{"className":5989},[614],[573,5991],{"className":5992,"style":619},[618],[573,5994,5996,6031],{"className":5995},[623],[573,5997,5999],{"className":5998},[623,3174],[573,6000,6002],{"className":6001},[635],[573,6003,6005],{"className":6004},[639],[573,6006,6008,6016],{"className":6007,"style":3170},[643],[573,6009,6010,6013],{"style":3186},[573,6011],{"className":6012,"style":3190},[650],[573,6014,3120],{"className":6015},[623,627],[573,6017,6018,6021],{"style":3186},[573,6019],{"className":6020,"style":3190},[650],[573,6022,6024],{"className":6023,"style":3203},[3202],[573,6025,6027],{"className":6026,"style":3208},[3207],[3210,6028,6029],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,6030],{"d":3221},[573,6032,6034],{"className":6033},[631],[573,6035,6037],{"className":6036},[635],[573,6038,6040],{"className":6039},[639],[573,6041,6043],{"className":6042,"style":619},[643],[573,6044,6045,6048],{"style":646},[573,6046],{"className":6047,"style":651},[650],[573,6049,6051],{"className":6050},[655,656,657,658],[573,6052,6054,6057],{"className":6053},[623,658],[573,6055],{"className":6056,"style":3352},[705,658],[573,6058,600],{"className":6059,"style":662},[623,627,658],[573,6061,6063],{"className":6062},[623,3174],[573,6064,6066],{"className":6065},[635],[573,6067,6069],{"className":6068},[639],[573,6070,6072,6080],{"className":6071,"style":3170},[643],[573,6073,6074,6077],{"style":3186},[573,6075],{"className":6076,"style":3190},[650],[573,6078,3131],{"className":6079,"style":3257},[623,627],[573,6081,6082,6085],{"style":3186},[573,6083],{"className":6084,"style":3190},[650],[573,6086,6088],{"className":6087,"style":3203},[3202],[573,6089,6091],{"className":6090,"style":3208},[3207],[3210,6092,6093],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,6094],{"d":3221}," (eine Zahl) mit ",[573,6097,6099,6133],{"className":6098},[576],[573,6100,6102],{"className":6101},[580],[582,6103,6104],{"xmlns":584},[586,6105,6106,6130],{},[589,6107,6108,6114,6116],{},[3116,6109,6110,6112],{"accent":610},[595,6111,3120],{},[680,6113,3123],{},[3147,6115,3149],{},[592,6117,6118,6124],{},[3116,6119,6120,6122],{"accent":610},[595,6121,3131],{},[680,6123,3123],{},[589,6125,6126,6128],{},[3147,6127,3149],{},[595,6129,600],{},[602,6131,6132],{"encoding":604},"\\vec u\\, \\vec v^{\\,T}",[573,6134,6136],{"className":6135,"ariaHidden":610},[609],[573,6137,6139,6142,6177,6180],{"className":6138},[614],[573,6140],{"className":6141,"style":619},[618],[573,6143,6145],{"className":6144},[623,3174],[573,6146,6148],{"className":6147},[635],[573,6149,6151],{"className":6150},[639],[573,6152,6154,6162],{"className":6153,"style":3170},[643],[573,6155,6156,6159],{"style":3186},[573,6157],{"className":6158,"style":3190},[650],[573,6160,3120],{"className":6161},[623,627],[573,6163,6164,6167],{"style":3186},[573,6165],{"className":6166,"style":3190},[650],[573,6168,6170],{"className":6169,"style":3203},[3202],[573,6171,6173],{"className":6172,"style":3208},[3207],[3210,6174,6175],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,6176],{"d":3221},[573,6178],{"className":6179,"style":2099},[705],[573,6181,6183,6218],{"className":6182},[623],[573,6184,6186],{"className":6185},[623,3174],[573,6187,6189],{"className":6188},[635],[573,6190,6192],{"className":6191},[639],[573,6193,6195,6203],{"className":6194,"style":3170},[643],[573,6196,6197,6200],{"style":3186},[573,6198],{"className":6199,"style":3190},[650],[573,6201,3131],{"className":6202,"style":3257},[623,627],[573,6204,6205,6208],{"style":3186},[573,6206],{"className":6207,"style":3190},[650],[573,6209,6211],{"className":6210,"style":3203},[3202],[573,6212,6214],{"className":6213,"style":3208},[3207],[3210,6215,6216],{"xmlns":3212,"width":3213,"height":3214,"style":3215,"viewBox":3216,"preserveAspectRatio":3217},[3219,6217],{"d":3221},[573,6219,6221],{"className":6220},[631],[573,6222,6224],{"className":6223},[635],[573,6225,6227],{"className":6226},[639],[573,6228,6230],{"className":6229,"style":619},[643],[573,6231,6232,6235],{"style":646},[573,6233],{"className":6234,"style":651},[650],[573,6236,6238],{"className":6237},[655,656,657,658],[573,6239,6241,6244],{"className":6240},[623,658],[573,6242],{"className":6243,"style":3352},[705,658],[573,6245,600],{"className":6246,"style":662},[623,627,658]," (eine ",[573,6249,6251,6269],{"className":6250},[576],[573,6252,6254],{"className":6253},[580],[582,6255,6256],{"xmlns":584},[586,6257,6258,6266],{},[589,6259,6260,6262,6264],{},[595,6261,685],{},[680,6263,682],{},[595,6265,685],{},[602,6267,6268],{"encoding":604},"n \\times n",[573,6270,6272,6290],{"className":6271,"ariaHidden":610},[609],[573,6273,6275,6278,6281,6284,6287],{"className":6274},[614],[573,6276],{"className":6277,"style":698},[618],[573,6279,685],{"className":6280},[623,627],[573,6282],{"className":6283,"style":706},[705],[573,6285,682],{"className":6286},[710],[573,6288],{"className":6289,"style":706},[705],[573,6291,6293,6296],{"className":6292},[614],[573,6294],{"className":6295,"style":720},[618],[573,6297,685],{"className":6298},[623,627],"-Matrix) verwechseln.",{"title":6301,"searchDepth":6302,"depth":6302,"links":6303},"",2,[6304,6305,6306],{"id":561,"depth":6302,"text":562},{"id":3394,"depth":6302,"text":3395},{"id":5579,"depth":6302,"text":5580},[6308,6311,6314,6317,6320,6322,6324,6326,6328,6330,6332,6334,6337],{"lhs":6309,"rhs":6310},"transpose(multiply([[a, b, c], [d, f, g]], [[p, q], [r, s], [u, v]]))[1, 1]","multiply(transpose([[p, q], [r, s], [u, v]]), transpose([[a, b, c], [d, f, g]]))[1, 1]",{"lhs":6312,"rhs":6313},"transpose(multiply([[a, b, c], [d, f, g]], [[p, q], [r, s], [u, v]]))[1, 2]","multiply(transpose([[p, q], [r, s], [u, v]]), transpose([[a, b, c], [d, f, g]]))[1, 2]",{"lhs":6315,"rhs":6316},"transpose(multiply([[a, b, c], [d, f, g]], [[p, q], [r, s], [u, v]]))[2, 1]","multiply(transpose([[p, q], [r, s], [u, v]]), transpose([[a, b, c], [d, f, g]]))[2, 1]",{"lhs":6318,"rhs":6319},"transpose(multiply([[a, b, c], [d, f, g]], [[p, q], [r, s], [u, v]]))[2, 2]","multiply(transpose([[p, q], [r, s], [u, v]]), transpose([[a, b, c], [d, f, g]]))[2, 2]",{"lhs":6321,"rhs":1770},"multiply([[1, 2], [3, 4]], [[0, 1], [1, 0]])[1, 2]",{"lhs":6323,"rhs":2362},"multiply([[1, 2], [3, 4]], [[0, 1], [1, 0]])[2, 1]",{"lhs":6325,"rhs":2258},"multiply([[0, 1], [1, 0]], [[1, 3], [2, 4]])[1, 1]",{"lhs":6327,"rhs":2362},"multiply([[0, 1], [1, 0]], [[1, 3], [2, 4]])[1, 2]",{"lhs":6329,"rhs":1770},"multiply([[0, 1], [1, 0]], [[1, 3], [2, 4]])[2, 1]",{"lhs":6331,"rhs":2263},"multiply([[0, 1], [1, 0]], [[1, 3], [2, 4]])[2, 2]",{"lhs":6333,"rhs":2263},"multiply([[1, 3], [2, 4]], [[0, 1], [1, 0]])[1, 1]",{"lhs":6335,"rhs":6336},"multiply(transpose([[a, b, c], [d, f, g]]), [[a, b, c], [d, f, g]])[1, 3]","multiply(transpose([[a, b, c], [d, f, g]]), [[a, b, c], [d, f, g]])[3, 1]",{"lhs":6338,"rhs":5337},"dot([1, 2, 2], [3, 0, 4])","A \\in \\mathbb{R}^{m \\times n},\\ B \\in \\mathbb{R}^{n \\times p},\\ C \\in \\mathbb{R}^{m \\times n}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\in \\mathbb{R}^{m \\times n},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9658em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003Cmi>B\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">B \\in \\mathbb{R}^{n \\times p},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\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:0.9658em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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>\u003Cmi>C\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>m\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">C \\in \\mathbb{R}^{m \\times n}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7713em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">m\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","transpose-rules","(AB)^{T} = B^{T} A^{T}, \\qquad (A + C)^{T} = A^{T} + C^{T}, \\qquad (A^{T})^{T} = A","\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>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>B\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsup>\u003Cmi>C\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(AB)^{T} = B^{T} A^{T}, \\qquad (A + C)^{T} = A^{T} + C^{T}, \\qquad (A^{T})^{T} = 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:1.1413em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\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:1.1413em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1413em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\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:0.9747em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:1.1413em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8913em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Frechenregeln-transponierte",[],[6352,6353,6354,6355],"matrix-multiplication","inverse-rules","orthogonal-matrix","symmetric-matrix-definiteness",{"title":548,"description":6301},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Frechenregeln-transponierte","Beim Transponieren eines Produkts dreht sich die Reihenfolge um; Summe und doppeltes Transponieren verhalten sich einfach.",[6360,6361,6362,2719],"transponierte","matrix","matrizenprodukt",[6364,6368],{"symbol":6365,"meaning":6366,"symbolHtml":6367},"A, B, C","Matrizen, deren Größen das Produkt AB und die Summe A + C erlauben","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A, B, C\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:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":6369,"meaning":6370,"symbolHtml":6371},"A^{T}","Transponierte von A, Eintrag (i, j) von A^T ist Eintrag (j, i) von A","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A^{T}\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:0.8413em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8413em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","r-n3QHd6WUOY1pcXDg41ko1_2XGp4y6uGl1vRJKHr20",[6374,6377,6380,6383],{"stem":6375,"title":6376,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdefinitheit-symmetrischer-matrizen","Definitheit symmetrischer Matrizen",{"stem":6378,"title":6379,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmatrizenmultiplikation","Matrizenmultiplikation",{"stem":6381,"title":6382,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Forthogonale-matrix","Orthogonale Matrix",{"stem":6384,"title":6385,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Frechenregeln-inverse","Rechenregeln für die Inverse",1793824279789]