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0 471 714","xMinYMin",[1151,1152],"path",{"d":1153},"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",[568,1155,1049],{"className":1156},[1157],"mpunct",[568,1159],{"className":1160,"style":1161},[708],"margin-right:0.1667em;",[568,1163,589],{"className":1164},[611,612],[568,1166,1168],{"className":1167},[611,1105],[568,1169,1172,1208],{"className":1170},[673,1171],"vlist-t2",[568,1173,1175,1203],{"className":1174},[677],[568,1176,1178,1187],{"className":1177,"style":1115},[681],[568,1179,1180,1183],{"style":1118},[568,1181],{"className":1182,"style":1122},[689],[568,1184,1056],{"className":1185,"style":1186},[611,612],"margin-right:0.0359em;",[568,1188,1189,1192],{"style":1118},[568,1190],{"className":1191,"style":1122},[689],[568,1193,1196],{"className":1194,"style":1195},[1134],"left:-0.1799em;",[568,1197,1199],{"className":1198,"style":1140},[1139],[1142,1200,1201],{"xmlns":1144,"width":1145,"height":1146,"style":1147,"viewBox":1148,"preserveAspectRatio":1149},[1151,1202],{"d":1153},[568,1204,1207],{"className":1205},[1206],"vlist-s","​",[568,1209,1211],{"className":1210},[677],[568,1212,1215],{"className":1213,"style":1214},[681],"height:0.1944em;",[568,1216],{},[568,1218,1061],{"className":1219},[1220],"mclose",[568,1222],{"className":1223,"style":709},[708],[568,1225,644],{"className":1226},[713],[568,1228],{"className":1229,"style":709},[708],[568,1231,1233,1236,1239,1274,1277,1280,1326],{"className":1232},[602],[568,1234],{"className":1235,"style":1094},[606],[568,1237,1035],{"className":1238},[1098],[568,1240,1242],{"className":1241},[611,1105],[568,1243,1245],{"className":1244},[673],[568,1246,1248],{"className":1247},[677],[568,1249,1251,1259],{"className":1250,"style":1115},[681],[568,1252,1253,1256],{"style":1118},[568,1254],{"className":1255,"style":1122},[689],[568,1257,1043],{"className":1258},[611,612],[568,1260,1261,1264],{"style":1118},[568,1262],{"className":1263,"style":1122},[689],[568,1265,1267],{"className":1266,"style":1135},[1134],[568,1268,1270],{"className":1269,"style":1140},[1139],[1142,1271,1272],{"xmlns":1144,"width":1145,"height":1146,"style":1147,"viewBox":1148,"preserveAspectRatio":1149},[1151,1273],{"d":1153},[568,1275,1049],{"className":1276},[1157],[568,1278],{"className":1279,"style":1161},[708],[568,1281,1283],{"className":1282},[611,1105],[568,1284,1286,1318],{"className":1285},[673,1171],[568,1287,1289,1315],{"className":1288},[677],[568,1290,1292,1300],{"className":1291,"style":1115},[681],[568,1293,1294,1297],{"style":1118},[568,1295],{"className":1296,"style":1122},[689],[568,1298,1056],{"className":1299,"style":1186},[611,612],[568,1301,1302,1305],{"style":1118},[568,1303],{"className":1304,"style":1122},[689],[568,1306,1308],{"className":1307,"style":1195},[1134],[568,1309,1311],{"className":1310,"style":1140},[1139],[1142,1312,1313],{"xmlns":1144,"width":1145,"height":1146,"style":1147,"viewBox":1148,"preserveAspectRatio":1149},[1151,1314],{"d":1153},[568,1316,1207],{"className":1317},[1206],[568,1319,1321],{"className":1320},[677],[568,1322,1324],{"className":1323,"style":1214},[681],[568,1325],{},[568,1327,1061],{"className":1328},[1220],", also auch Längen und Winkel.",[564,1331,1332],{},"Weitere Eigenschaften:",[730,1334,1335,1517,1520],{},[733,1336,1337,1409,1410,1445,1446,1474,1475,1478,1479,1513,1514,988],{},[568,1338,1340,1367],{"className":1339},[571],[568,1341,1343],{"className":1342},[575],[577,1344,1345],{"xmlns":579},[581,1346,1347,1364],{},[584,1348,1349,1352,1355,1357,1359,1362],{},[587,1350,1351],{},"det",[642,1353,1354],{},"⁡",[587,1356,589],{},[642,1358,644],{},[642,1360,1361],{},"±",[782,1363,784],{},[591,1365,1366],{"encoding":593},"\\det Q = \\pm 1",[568,1368,1370,1396],{"className":1369,"ariaHidden":598},[597],[568,1371,1373,1377,1381,1384,1387,1390,1393],{"className":1372},[602],[568,1374],{"className":1375,"style":1376},[606],"height:0.8889em;vertical-align:-0.1944em;",[568,1378,1351],{"className":1379},[1380],"mop",[568,1382],{"className":1383,"style":1161},[708],[568,1385,589],{"className":1386},[611,612],[568,1388],{"className":1389,"style":709},[708],[568,1391,644],{"className":1392},[713],[568,1394],{"className":1395,"style":709},[708],[568,1397,1399,1403,1406],{"className":1398},[602],[568,1400],{"className":1401,"style":1402},[606],"height:0.7278em;vertical-align:-0.0833em;",[568,1404,1361],{"className":1405},[611],[568,1407,784],{"className":1408},[611],". Bei ",[568,1411,1413,1430],{"className":1412},[571],[568,1414,1416],{"className":1415},[575],[577,1417,1418],{"xmlns":579},[581,1419,1420,1427],{},[584,1421,1422,1425],{},[642,1423,1424],{},"+",[782,1426,784],{},[591,1428,1429],{"encoding":593},"+1",[568,1431,1433],{"className":1432,"ariaHidden":598},[597],[568,1434,1436,1439,1442],{"className":1435},[602],[568,1437],{"className":1438,"style":1402},[606],[568,1440,1424],{"className":1441},[611],[568,1443,784],{"className":1444},[611]," ist ",[568,1447,1449,1462],{"className":1448},[571],[568,1450,1452],{"className":1451},[575],[577,1453,1454],{"xmlns":579},[581,1455,1456,1460],{},[584,1457,1458],{},[587,1459,589],{},[591,1461,589],{"encoding":593},[568,1463,1465],{"className":1464,"ariaHidden":598},[597],[568,1466,1468,1471],{"className":1467},[602],[568,1469],{"className":1470,"style":607},[606],[568,1472,589],{"className":1473},[611,612]," eine ",[615,1476,1477],{},"Drehung",", bei ",[568,1480,1482,1498],{"className":1481},[571],[568,1483,1485],{"className":1484},[575],[577,1486,1487],{"xmlns":579},[581,1488,1489,1495],{},[584,1490,1491,1493],{},[642,1492,884],{},[782,1494,784],{},[591,1496,1497],{"encoding":593},"-1",[568,1499,1501],{"className":1500,"ariaHidden":598},[597],[568,1502,1504,1507,1510],{"className":1503},[602],[568,1505],{"className":1506,"style":1402},[606],[568,1508,884],{"className":1509},[611],[568,1511,784],{"className":1512},[611]," enthält sie eine ",[615,1515,1516],{},"Spiegelung",[733,1518,1519],{},"Produkte und Inverse orthogonaler Matrizen sind wieder orthogonal.",[733,1521,1522,1523,1557,1558,988],{},"Reelle Eigenwerte sind ",[568,1524,1526,1542],{"className":1525},[571],[568,1527,1529],{"className":1528},[575],[577,1530,1531],{"xmlns":579},[581,1532,1533,1539],{},[584,1534,1535,1537],{},[642,1536,1361],{},[782,1538,784],{},[591,1540,1541],{"encoding":593},"\\pm 1",[568,1543,1545],{"className":1544,"ariaHidden":598},[597],[568,1546,1548,1551,1554],{"className":1547},[602],[568,1549],{"className":1550,"style":1402},[606],[568,1552,1361],{"className":1553},[611],[568,1555,784],{"className":1556},[611],", komplexe haben den Betrag ",[568,1559,1561,1574],{"className":1560},[571],[568,1562,1564],{"className":1563},[575],[577,1565,1566],{"xmlns":579},[581,1567,1568,1572],{},[584,1569,1570],{},[782,1571,784],{},[591,1573,784],{"encoding":593},[568,1575,1577],{"className":1576,"ariaHidden":598},[597],[568,1578,1580,1583],{"className":1579},[602],[568,1581],{"className":1582,"style":796},[606],[568,1584,784],{"className":1585},[611],[564,1587,1588],{},"Orthogonale Matrizen sind numerisch angenehm: Die Inverse kostet nur ein Transponieren, und Rundungsfehler werden nicht verstärkt. Deshalb tauchen sie in der QR-Zerlegung und bei der Diagonalisierung symmetrischer Matrizen auf.",[559,1590,1592],{"id":1591},"beispiele","Beispiele",[564,1594,1595,1912,1913,1994,1995,2075,2076,2104,2105,2203,2204,2302,2303,2331,2332,2393,2394,2451,2452,2509,2510,988],{},[568,1596,1598,1674],{"className":1597},[571],[568,1599,1601],{"className":1600},[575],[577,1602,1603],{"xmlns":579},[581,1604,1605,1671],{},[584,1606,1607,1609,1611,1619],{},[587,1608,589],{},[642,1610,644],{},[1612,1613,1614,1616],"mfrac",{},[782,1615,784],{},[782,1617,1618],{},"5",[584,1620,1621,1624,1668],{},[642,1622,1623],{"fence":598},"(",[1625,1626,1630,1654],"mtable",{"rowspacing":1627,"columnalign":1628,"columnspacing":1629},"0.16em","center center","1em",[1631,1632,1633,1643],"mtr",{},[1634,1635,1636],"mtd",{},[1637,1638,1640],"mstyle",{"scriptlevel":1639,"displaystyle":1034},"0",[782,1641,1642],{},"3",[1634,1644,1645],{},[1637,1646,1647],{"scriptlevel":1639,"displaystyle":1034},[584,1648,1649,1651],{},[642,1650,884],{},[782,1652,1653],{},"4",[1631,1655,1656,1662],{},[1634,1657,1658],{},[1637,1659,1660],{"scriptlevel":1639,"displaystyle":1034},[782,1661,1653],{},[1634,1663,1664],{},[1637,1665,1666],{"scriptlevel":1639,"displaystyle":1034},[782,1667,1642],{},[642,1669,1670],{"fence":598},")",[591,1672,1673],{"encoding":593},"Q = \\frac{1}{5}\\begin{pmatrix} 3 & -4 \\\\ 4 & 3 \\end{pmatrix}",[568,1675,1677,1695],{"className":1676,"ariaHidden":598},[597],[568,1678,1680,1683,1686,1689,1692],{"className":1679},[602],[568,1681],{"className":1682,"style":607},[606],[568,1684,589],{"className":1685},[611,612],[568,1687],{"className":1688,"style":709},[708],[568,1690,644],{"className":1691},[713],[568,1693],{"className":1694,"style":709},[708],[568,1696,1698,1702,1778,1781],{"className":1697},[602],[568,1699],{"className":1700,"style":1701},[606],"height:2.4em;vertical-align:-0.95em;",[568,1703,1705,1709,1775],{"className":1704},[611],[568,1706],{"className":1707},[1098,1708],"nulldelimiter",[568,1710,1712],{"className":1711},[1612],[568,1713,1715,1766],{"className":1714},[673,1171],[568,1716,1718,1763],{"className":1717},[677],[568,1719,1722,1737,1748],{"className":1720,"style":1721},[681],"height:0.8451em;",[568,1723,1725,1728],{"style":1724},"top:-2.655em;",[568,1726],{"className":1727,"style":1122},[689],[568,1729,1731],{"className":1730},[694,695,696,697],[568,1732,1734],{"className":1733},[611,697],[568,1735,1618],{"className":1736},[611,697],[568,1738,1740,1743],{"style":1739},"top:-3.23em;",[568,1741],{"className":1742,"style":1122},[689],[568,1744],{"className":1745,"style":1747},[1746],"frac-line","border-bottom-width:0.04em;",[568,1749,1751,1754],{"style":1750},"top:-3.394em;",[568,1752],{"className":1753,"style":1122},[689],[568,1755,1757],{"className":1756},[694,695,696,697],[568,1758,1760],{"className":1759},[611,697],[568,1761,784],{"className":1762},[611,697],[568,1764,1207],{"className":1765},[1206],[568,1767,1769],{"className":1768},[677],[568,1770,1773],{"className":1771,"style":1772},[681],"height:0.345em;",[568,1774],{},[568,1776],{"className":1777},[1220,1708],[568,1779],{"className":1780,"style":1161},[708],[568,1782,1785,1794,1906],{"className":1783},[1784],"minner",[568,1786,1790],{"className":1787,"style":1789},[1098,1788],"delimcenter","top:0em;",[568,1791,1623],{"className":1792},[1793,696],"delimsizing",[568,1795,1797],{"className":1796},[611],[568,1798,1800,1850,1855,1858],{"className":1799},[1625],[568,1801,1804],{"className":1802},[1803],"col-align-c",[568,1805,1807,1841],{"className":1806},[673,1171],[568,1808,1810,1838],{"className":1809},[677],[568,1811,1814,1826],{"className":1812,"style":1813},[681],"height:1.45em;",[568,1815,1817,1820],{"style":1816},"top:-3.61em;",[568,1818],{"className":1819,"style":1122},[689],[568,1821,1823],{"className":1822},[611],[568,1824,1642],{"className":1825},[611],[568,1827,1829,1832],{"style":1828},"top:-2.41em;",[568,1830],{"className":1831,"style":1122},[689],[568,1833,1835],{"className":1834},[611],[568,1836,1653],{"className":1837},[611],[568,1839,1207],{"className":1840},[1206],[568,1842,1844],{"className":1843},[677],[568,1845,1848],{"className":1846,"style":1847},[681],"height:0.95em;",[568,1849],{},[568,1851],{"className":1852,"style":1854},[1853],"arraycolsep","width:0.5em;",[568,1856],{"className":1857,"style":1854},[1853],[568,1859,1861],{"className":1860},[1803],[568,1862,1864,1898],{"className":1863},[673,1171],[568,1865,1867,1895],{"className":1866},[677],[568,1868,1870,1884],{"className":1869,"style":1813},[681],[568,1871,1872,1875],{"style":1816},[568,1873],{"className":1874,"style":1122},[689],[568,1876,1878,1881],{"className":1877},[611],[568,1879,884],{"className":1880},[611],[568,1882,1653],{"className":1883},[611],[568,1885,1886,1889],{"style":1828},[568,1887],{"className":1888,"style":1122},[689],[568,1890,1892],{"className":1891},[611],[568,1893,1642],{"className":1894},[611],[568,1896,1207],{"className":1897},[1206],[568,1899,1901],{"className":1900},[677],[568,1902,1904],{"className":1903,"style":1847},[681],[568,1905],{},[568,1907,1909],{"className":1908,"style":1789},[1220,1788],[568,1910,1670],{"className":1911},[1793,696],": Die Spalten ",[568,1914,1916,1944],{"className":1915},[571],[568,1917,1919],{"className":1918},[575],[577,1920,1921],{"xmlns":579},[581,1922,1923,1941],{},[584,1924,1925,1927,1930,1932,1936,1939],{},[642,1926,1623],{"stretchy":1034},[782,1928,1929],{},"0,6",[642,1931,1049],{"separator":598},[1933,1934,1935],"mtext",{}," ",[782,1937,1938],{},"0,8",[642,1940,1670],{"stretchy":1034},[591,1942,1943],{"encoding":593},"(0{,}6,\\ 0{,}8)",[568,1945,1947],{"className":1946,"ariaHidden":598},[597],[568,1948,1950,1953,1956,1959,1965,1969,1972,1975,1978,1981,1987,1991],{"className":1949},[602],[568,1951],{"className":1952,"style":1094},[606],[568,1954,1623],{"className":1955},[1098],[568,1957,1639],{"className":1958},[611],[568,1960,1962],{"className":1961},[611],[568,1963,1049],{"className":1964},[1157],[568,1966,1968],{"className":1967},[611],"6",[568,1970,1049],{"className":1971},[1157],[568,1973,1935],{"className":1974},[708],[568,1976],{"className":1977,"style":1161},[708],[568,1979,1639],{"className":1980},[611],[568,1982,1984],{"className":1983},[611],[568,1985,1049],{"className":1986},[1157],[568,1988,1990],{"className":1989},[611],"8",[568,1992,1670],{"className":1993},[1220]," und ",[568,1996,1998,2024],{"className":1997},[571],[568,1999,2001],{"className":2000},[575],[577,2002,2003],{"xmlns":579},[581,2004,2005,2021],{},[584,2006,2007,2009,2011,2013,2015,2017,2019],{},[642,2008,1623],{"stretchy":1034},[642,2010,884],{},[782,2012,1938],{},[642,2014,1049],{"separator":598},[1933,2016,1935],{},[782,2018,1929],{},[642,2020,1670],{"stretchy":1034},[591,2022,2023],{"encoding":593},"(-0{,}8,\\ 0{,}6)",[568,2025,2027],{"className":2026,"ariaHidden":598},[597],[568,2028,2030,2033,2036,2039,2042,2048,2051,2054,2057,2060,2063,2069,2072],{"className":2029},[602],[568,2031],{"className":2032,"style":1094},[606],[568,2034,1623],{"className":2035},[1098],[568,2037,884],{"className":2038},[611],[568,2040,1639],{"className":2041},[611],[568,2043,2045],{"className":2044},[611],[568,2046,1049],{"className":2047},[1157],[568,2049,1990],{"className":2050},[611],[568,2052,1049],{"className":2053},[1157],[568,2055,1935],{"className":2056},[708],[568,2058],{"className":2059,"style":1161},[708],[568,2061,1639],{"className":2062},[611],[568,2064,2066],{"className":2065},[611],[568,2067,1049],{"className":2068},[1157],[568,2070,1968],{"className":2071},[611],[568,2073,1670],{"className":2074},[1220]," haben Länge ",[568,2077,2079,2092],{"className":2078},[571],[568,2080,2082],{"className":2081},[575],[577,2083,2084],{"xmlns":579},[581,2085,2086,2090],{},[584,2087,2088],{},[782,2089,784],{},[591,2091,784],{"encoding":593},[568,2093,2095],{"className":2094,"ariaHidden":598},[597],[568,2096,2098,2101],{"className":2097},[602],[568,2099],{"className":2100,"style":796},[606],[568,2102,784],{"className":2103},[611],", denn ",[568,2106,2108,2132],{"className":2107},[571],[568,2109,2111],{"className":2110},[575],[577,2112,2113],{"xmlns":579},[581,2114,2115,2129],{},[584,2116,2117,2120,2122,2125,2127],{},[782,2118,2119],{},"0,36",[642,2121,1424],{},[782,2123,2124],{},"0,64",[642,2126,644],{},[782,2128,784],{},[591,2130,2131],{"encoding":593},"0{,}36 + 0{,}64 = 1",[568,2133,2135,2166,2194],{"className":2134,"ariaHidden":598},[597],[568,2136,2138,2142,2145,2151,2155,2159,2163],{"className":2137},[602],[568,2139],{"className":2140,"style":2141},[606],"height:0.8389em;vertical-align:-0.1944em;",[568,2143,1639],{"className":2144},[611],[568,2146,2148],{"className":2147},[611],[568,2149,1049],{"className":2150},[1157],[568,2152,2154],{"className":2153},[611],"36",[568,2156],{"className":2157,"style":2158},[708],"margin-right:0.2222em;",[568,2160,1424],{"className":2161},[2162],"mbin",[568,2164],{"className":2165,"style":2158},[708],[568,2167,2169,2172,2175,2181,2185,2188,2191],{"className":2168},[602],[568,2170],{"className":2171,"style":2141},[606],[568,2173,1639],{"className":2174},[611],[568,2176,2178],{"className":2177},[611],[568,2179,1049],{"className":2180},[1157],[568,2182,2184],{"className":2183},[611],"64",[568,2186],{"className":2187,"style":709},[708],[568,2189,644],{"className":2190},[713],[568,2192],{"className":2193,"style":709},[708],[568,2195,2197,2200],{"className":2196},[602],[568,2198],{"className":2199,"style":796},[606],[568,2201,784],{"className":2202},[611],", und ihr Skalarprodukt ist ",[568,2205,2207,2232],{"className":2206},[571],[568,2208,2210],{"className":2209},[575],[577,2211,2212],{"xmlns":579},[581,2213,2214,2229],{},[584,2215,2216,2218,2221,2223,2225,2227],{},[642,2217,884],{},[782,2219,2220],{},"0,48",[642,2222,1424],{},[782,2224,2220],{},[642,2226,644],{},[782,2228,1639],{},[591,2230,2231],{"encoding":593},"-0{,}48 + 0{,}48 = 0",[568,2233,2235,2266,2293],{"className":2234,"ariaHidden":598},[597],[568,2236,2238,2241,2244,2247,2253,2257,2260,2263],{"className":2237},[602],[568,2239],{"className":2240,"style":2141},[606],[568,2242,884],{"className":2243},[611],[568,2245,1639],{"className":2246},[611],[568,2248,2250],{"className":2249},[611],[568,2251,1049],{"className":2252},[1157],[568,2254,2256],{"className":2255},[611],"48",[568,2258],{"className":2259,"style":2158},[708],[568,2261,1424],{"className":2262},[2162],[568,2264],{"className":2265,"style":2158},[708],[568,2267,2269,2272,2275,2281,2284,2287,2290],{"className":2268},[602],[568,2270],{"className":2271,"style":2141},[606],[568,2273,1639],{"className":2274},[611],[568,2276,2278],{"className":2277},[611],[568,2279,1049],{"className":2280},[1157],[568,2282,2256],{"className":2283},[611],[568,2285],{"className":2286,"style":709},[708],[568,2288,644],{"className":2289},[713],[568,2291],{"className":2292,"style":709},[708],[568,2294,2296,2299],{"className":2295},[602],[568,2297],{"className":2298,"style":796},[606],[568,2300,1639],{"className":2301},[611],". Also ist ",[568,2304,2306,2319],{"className":2305},[571],[568,2307,2309],{"className":2308},[575],[577,2310,2311],{"xmlns":579},[581,2312,2313,2317],{},[584,2314,2315],{},[587,2316,589],{},[591,2318,589],{"encoding":593},[568,2320,2322],{"className":2321,"ariaHidden":598},[597],[568,2323,2325,2328],{"className":2324},[602],[568,2326],{"className":2327,"style":607},[606],[568,2329,589],{"className":2330},[611,612]," orthogonal mit ",[568,2333,2335,2357],{"className":2334},[571],[568,2336,2338],{"className":2337},[575],[577,2339,2340],{"xmlns":579},[581,2341,2342,2354],{},[584,2343,2344,2346,2348,2350,2352],{},[587,2345,1351],{},[642,2347,1354],{},[587,2349,589],{},[642,2351,644],{},[782,2353,784],{},[591,2355,2356],{"encoding":593},"\\det Q = 1",[568,2358,2360,2384],{"className":2359,"ariaHidden":598},[597],[568,2361,2363,2366,2369,2372,2375,2378,2381],{"className":2362},[602],[568,2364],{"className":2365,"style":1376},[606],[568,2367,1351],{"className":2368},[1380],[568,2370],{"className":2371,"style":1161},[708],[568,2373,589],{"className":2374},[611,612],[568,2376],{"className":2377,"style":709},[708],[568,2379,644],{"className":2380},[713],[568,2382],{"className":2383,"style":709},[708],[568,2385,2387,2390],{"className":2386},[602],[568,2388],{"className":2389,"style":796},[606],[568,2391,784],{"className":2392},[611],", eine Drehung. Sie bildet ",[568,2395,2397,2421],{"className":2396},[571],[568,2398,2400],{"className":2399},[575],[577,2401,2402],{"xmlns":579},[581,2403,2404,2418],{},[584,2405,2406,2408,2410,2412,2414,2416],{},[642,2407,1623],{"stretchy":1034},[782,2409,1618],{},[642,2411,1049],{"separator":598},[1933,2413,1935],{},[782,2415,1639],{},[642,2417,1670],{"stretchy":1034},[591,2419,2420],{"encoding":593},"(5,\\ 0)",[568,2422,2424],{"className":2423,"ariaHidden":598},[597],[568,2425,2427,2430,2433,2436,2439,2442,2445,2448],{"className":2426},[602],[568,2428],{"className":2429,"style":1094},[606],[568,2431,1623],{"className":2432},[1098],[568,2434,1618],{"className":2435},[611],[568,2437,1049],{"className":2438},[1157],[568,2440,1935],{"className":2441},[708],[568,2443],{"className":2444,"style":1161},[708],[568,2446,1639],{"className":2447},[611],[568,2449,1670],{"className":2450},[1220]," auf ",[568,2453,2455,2479],{"className":2454},[571],[568,2456,2458],{"className":2457},[575],[577,2459,2460],{"xmlns":579},[581,2461,2462,2476],{},[584,2463,2464,2466,2468,2470,2472,2474],{},[642,2465,1623],{"stretchy":1034},[782,2467,1642],{},[642,2469,1049],{"separator":598},[1933,2471,1935],{},[782,2473,1653],{},[642,2475,1670],{"stretchy":1034},[591,2477,2478],{"encoding":593},"(3,\\ 4)",[568,2480,2482],{"className":2481,"ariaHidden":598},[597],[568,2483,2485,2488,2491,2494,2497,2500,2503,2506],{"className":2484},[602],[568,2486],{"className":2487,"style":1094},[606],[568,2489,1623],{"className":2490},[1098],[568,2492,1642],{"className":2493},[611],[568,2495,1049],{"className":2496},[1157],[568,2498,1935],{"className":2499},[708],[568,2501],{"className":2502,"style":1161},[708],[568,2504,1653],{"className":2505},[611],[568,2507,1670],{"className":2508},[1220]," ab, beide haben Länge ",[568,2511,2513,2526],{"className":2512},[571],[568,2514,2516],{"className":2515},[575],[577,2517,2518],{"xmlns":579},[581,2519,2520,2524],{},[584,2521,2522],{},[782,2523,1618],{},[591,2525,1618],{"encoding":593},[568,2527,2529],{"className":2528,"ariaHidden":598},[597],[568,2530,2532,2535],{"className":2531},[602],[568,2533],{"className":2534,"style":796},[606],[568,2536,1618],{"className":2537},[611],[564,2539,2540,2541,2935,2936,3003,3004,988],{},"Die Permutationsmatrix ",[568,2542,2544,2630],{"className":2543},[571],[568,2545,2547],{"className":2546},[575],[577,2548,2549],{"xmlns":579},[581,2550,2551,2627],{},[584,2552,2553,2556,2558],{},[587,2554,2555],{},"P",[642,2557,644],{},[584,2559,2560,2562,2625],{},[642,2561,1623],{"fence":598},[1625,2563,2565,2585,2605],{"rowspacing":1627,"columnalign":2564,"columnspacing":1629},"center center center",[1631,2566,2567,2573,2579],{},[1634,2568,2569],{},[1637,2570,2571],{"scriptlevel":1639,"displaystyle":1034},[782,2572,1639],{},[1634,2574,2575],{},[1637,2576,2577],{"scriptlevel":1639,"displaystyle":1034},[782,2578,784],{},[1634,2580,2581],{},[1637,2582,2583],{"scriptlevel":1639,"displaystyle":1034},[782,2584,1639],{},[1631,2586,2587,2593,2599],{},[1634,2588,2589],{},[1637,2590,2591],{"scriptlevel":1639,"displaystyle":1034},[782,2592,784],{},[1634,2594,2595],{},[1637,2596,2597],{"scriptlevel":1639,"displaystyle":1034},[782,2598,1639],{},[1634,2600,2601],{},[1637,2602,2603],{"scriptlevel":1639,"displaystyle":1034},[782,2604,1639],{},[1631,2606,2607,2613,2619],{},[1634,2608,2609],{},[1637,2610,2611],{"scriptlevel":1639,"displaystyle":1034},[782,2612,1639],{},[1634,2614,2615],{},[1637,2616,2617],{"scriptlevel":1639,"displaystyle":1034},[782,2618,1639],{},[1634,2620,2621],{},[1637,2622,2623],{"scriptlevel":1639,"displaystyle":1034},[782,2624,784],{},[642,2626,1670],{"fence":598},[591,2628,2629],{"encoding":593},"P = \\begin{pmatrix} 0 & 1 & 0 \\\\ 1 & 0 & 0 \\\\ 0 & 0 & 1 \\end{pmatrix}",[568,2631,2633,2651],{"className":2632,"ariaHidden":598},[597],[568,2634,2636,2639,2642,2645,2648],{"className":2635},[602],[568,2637],{"className":2638,"style":723},[606],[568,2640,2555],{"className":2641,"style":701},[611,612],[568,2643],{"className":2644,"style":709},[708],[568,2646,644],{"className":2647},[713],[568,2649],{"className":2650,"style":709},[708],[568,2652,2654,2658],{"className":2653},[602],[568,2655],{"className":2656,"style":2657},[606],"height:3.6em;vertical-align:-1.55em;",[568,2659,2661,2708,2897],{"className":2660},[1784],[568,2662,2664],{"className":2663},[1098],[568,2665,2668],{"className":2666},[1793,2667],"mult",[568,2669,2671,2699],{"className":2670},[673,1171],[568,2672,2674,2696],{"className":2673},[677],[568,2675,2678],{"className":2676,"style":2677},[681],"height:2.05em;",[568,2679,2681,2685],{"style":2680},"top:-4.05em;",[568,2682],{"className":2683,"style":2684},[689],"height:5.6em;",[568,2686,2688],{"style":2687},"width:0.875em;height:3.6em;",[1142,2689,2693],{"xmlns":1144,"width":2690,"height":2691,"viewBox":2692},"0.875em","3.6em","0 0 875 3600",[1151,2694],{"d":2695},"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 l0,84c0.2,6,0,26,0,60c2,159.3,10,310.7,24,454c53.3,528,210,\n949.7,470,1265c4.7,6,9.7,11.7,15,17c0.7,0.7,7,1,19,1c0,0,18,0,18,0c4,-4,6,-7,6,-9\nc0,-2.7,-3.3,-8.7,-10,-18c-135.3,-192.7,-235.5,-414.3,-300.5,-665c-65,-250.7,-102.5,\n-544.7,-112.5,-882c-2,-104,-3,-167,-3,-189\nl0,-92c0,-162.7,5.7,-314,17,-454c20.7,-272,63.7,-513,129,-723c65.3,\n-210,155.3,-396.3,270,-559c6.7,-9.3,10,-15.3,10,-18z",[568,2697,1207],{"className":2698},[1206],[568,2700,2702],{"className":2701},[677],[568,2703,2706],{"className":2704,"style":2705},[681],"height:1.55em;",[568,2707],{},[568,2709,2711],{"className":2710},[611],[568,2712,2714,2773,2776,2779,2835,2838,2841],{"className":2713},[1625],[568,2715,2717],{"className":2716},[1803],[568,2718,2720,2765],{"className":2719},[673,1171],[568,2721,2723,2762],{"className":2722},[677],[568,2724,2726,2738,2750],{"className":2725,"style":2677},[681],[568,2727,2729,2732],{"style":2728},"top:-4.21em;",[568,2730],{"className":2731,"style":1122},[689],[568,2733,2735],{"className":2734},[611],[568,2736,1639],{"className":2737},[611],[568,2739,2741,2744],{"style":2740},"top:-3.01em;",[568,2742],{"className":2743,"style":1122},[689],[568,2745,2747],{"className":2746},[611],[568,2748,784],{"className":2749},[611],[568,2751,2753,2756],{"style":2752},"top:-1.81em;",[568,2754],{"className":2755,"style":1122},[689],[568,2757,2759],{"className":2758},[611],[568,2760,1639],{"className":2761},[611],[568,2763,1207],{"className":2764},[1206],[568,2766,2768],{"className":2767},[677],[568,2769,2771],{"className":2770,"style":2705},[681],[568,2772],{},[568,2774],{"className":2775,"style":1854},[1853],[568,2777],{"className":2778,"style":1854},[1853],[568,2780,2782],{"className":2781},[1803],[568,2783,2785,2827],{"className":2784},[673,1171],[568,2786,2788,2824],{"className":2787},[677],[568,2789,2791,2802,2813],{"className":2790,"style":2677},[681],[568,2792,2793,2796],{"style":2728},[568,2794],{"className":2795,"style":1122},[689],[568,2797,2799],{"className":2798},[611],[568,2800,784],{"className":2801},[611],[568,2803,2804,2807],{"style":2740},[568,2805],{"className":2806,"style":1122},[689],[568,2808,2810],{"className":2809},[611],[568,2811,1639],{"className":2812},[611],[568,2814,2815,2818],{"style":2752},[568,2816],{"className":2817,"style":1122},[689],[568,2819,2821],{"className":2820},[611],[568,2822,1639],{"className":2823},[611],[568,2825,1207],{"className":2826},[1206],[568,2828,2830],{"className":2829},[677],[568,2831,2833],{"className":2832,"style":2705},[681],[568,2834],{},[568,2836],{"className":2837,"style":1854},[1853],[568,2839],{"className":2840,"style":1854},[1853],[568,2842,2844],{"className":2843},[1803],[568,2845,2847,2889],{"className":2846},[673,1171],[568,2848,2850,2886],{"className":2849},[677],[568,2851,2853,2864,2875],{"className":2852,"style":2677},[681],[568,2854,2855,2858],{"style":2728},[568,2856],{"className":2857,"style":1122},[689],[568,2859,2861],{"className":2860},[611],[568,2862,1639],{"className":2863},[611],[568,2865,2866,2869],{"style":2740},[568,2867],{"className":2868,"style":1122},[689],[568,2870,2872],{"className":2871},[611],[568,2873,1639],{"className":2874},[611],[568,2876,2877,2880],{"style":2752},[568,2878],{"className":2879,"style":1122},[689],[568,2881,2883],{"className":2882},[611],[568,2884,784],{"className":2885},[611],[568,2887,1207],{"className":2888},[1206],[568,2890,2892],{"className":2891},[677],[568,2893,2895],{"className":2894,"style":2705},[681],[568,2896],{},[568,2898,2900],{"className":2899},[1220],[568,2901,2903],{"className":2902},[1793,2667],[568,2904,2906,2927],{"className":2905},[673,1171],[568,2907,2909,2924],{"className":2908},[677],[568,2910,2912],{"className":2911,"style":2677},[681],[568,2913,2914,2917],{"style":2680},[568,2915],{"className":2916,"style":2684},[689],[568,2918,2919],{"style":2687},[1142,2920,2921],{"xmlns":1144,"width":2690,"height":2691,"viewBox":2692},[1151,2922],{"d":2923},"M76,0c-16.7,0,-25,3,-25,9c0,2,2,6.3,6,13c21.3,28.7,42.3,60.3,\n63,95c96.7,156.7,172.8,332.5,228.5,527.5c55.7,195,92.8,416.5,111.5,664.5\nc11.3,139.3,17,290.7,17,454c0,28,1.7,43,3.3,45l0,9\nc-3,4,-3.3,16.7,-3.3,38c0,162,-5.7,313.7,-17,455c-18.7,248,-55.8,469.3,-111.5,664\nc-55.7,194.7,-131.8,370.3,-228.5,527c-20.7,34.7,-41.7,66.3,-63,95c-2,3.3,-4,7,-6,11\nc0,7.3,5.7,11,17,11c0,0,11,0,11,0c9.3,0,14.3,-0.3,15,-1c5.3,-5.3,10.3,-11,15,-17\nc242.7,-294.7,395.3,-681.7,458,-1161c21.3,-164.7,33.3,-350.7,36,-558\nl0,-144c-2,-159.3,-10,-310.7,-24,-454c-53.3,-528,-210,-949.7,\n-470,-1265c-4.7,-6,-9.7,-11.7,-15,-17c-0.7,-0.7,-6.7,-1,-18,-1z",[568,2925,1207],{"className":2926},[1206],[568,2928,2930],{"className":2929},[677],[568,2931,2933],{"className":2932,"style":2705},[681],[568,2934],{}," vertauscht die ersten beiden Koordinaten. Sie ist orthogonal mit ",[568,2937,2939,2963],{"className":2938},[571],[568,2940,2942],{"className":2941},[575],[577,2943,2944],{"xmlns":579},[581,2945,2946,2960],{},[584,2947,2948,2950,2952,2954,2956,2958],{},[587,2949,1351],{},[642,2951,1354],{},[587,2953,2555],{},[642,2955,644],{},[642,2957,884],{},[782,2959,784],{},[591,2961,2962],{"encoding":593},"\\det P = -1",[568,2964,2966,2991],{"className":2965,"ariaHidden":598},[597],[568,2967,2969,2973,2976,2979,2982,2985,2988],{"className":2968},[602],[568,2970],{"className":2971,"style":2972},[606],"height:0.6944em;",[568,2974,1351],{"className":2975},[1380],[568,2977],{"className":2978,"style":1161},[708],[568,2980,2555],{"className":2981,"style":701},[611,612],[568,2983],{"className":2984,"style":709},[708],[568,2986,644],{"className":2987},[713],[568,2989],{"className":2990,"style":709},[708],[568,2992,2994,2997,3000],{"className":2993},[602],[568,2995],{"className":2996,"style":1402},[606],[568,2998,884],{"className":2999},[611],[568,3001,784],{"className":3002},[611],", eine Spiegelung an der Ebene ",[568,3005,3007,3035],{"className":3006},[571],[568,3008,3010],{"className":3009},[575],[577,3011,3012],{"xmlns":579},[581,3013,3014,3032],{},[584,3015,3016,3023,3025],{},[3017,3018,3019,3021],"msub",{},[587,3020,1043],{},[782,3022,784],{},[642,3024,644],{},[3017,3026,3027,3029],{},[587,3028,1043],{},[782,3030,3031],{},"2",[591,3033,3034],{"encoding":593},"x_1 = x_2",[568,3036,3038,3097],{"className":3037,"ariaHidden":598},[597],[568,3039,3041,3045,3088,3091,3094],{"className":3040},[602],[568,3042],{"className":3043,"style":3044},[606],"height:0.5806em;vertical-align:-0.15em;",[568,3046,3048,3051],{"className":3047},[611],[568,3049,1043],{"className":3050},[611,612],[568,3052,3054],{"className":3053},[669],[568,3055,3057,3079],{"className":3056},[673,1171],[568,3058,3060,3076],{"className":3059},[677],[568,3061,3064],{"className":3062,"style":3063},[681],"height:0.3011em;",[568,3065,3067,3070],{"style":3066},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[568,3068],{"className":3069,"style":690},[689],[568,3071,3073],{"className":3072},[694,695,696,697],[568,3074,784],{"className":3075},[611,697],[568,3077,1207],{"className":3078},[1206],[568,3080,3082],{"className":3081},[677],[568,3083,3086],{"className":3084,"style":3085},[681],"height:0.15em;",[568,3087],{},[568,3089],{"className":3090,"style":709},[708],[568,3092,644],{"className":3093},[713],[568,3095],{"className":3096,"style":709},[708],[568,3098,3100,3103],{"className":3099},[602],[568,3101],{"className":3102,"style":3044},[606],[568,3104,3106,3109],{"className":3105},[611],[568,3107,1043],{"className":3108},[611,612],[568,3110,3112],{"className":3111},[669],[568,3113,3115,3135],{"className":3114},[673,1171],[568,3116,3118,3132],{"className":3117},[677],[568,3119,3121],{"className":3120,"style":3063},[681],[568,3122,3123,3126],{"style":3066},[568,3124],{"className":3125,"style":690},[689],[568,3127,3129],{"className":3128},[694,695,696,697],[568,3130,3031],{"className":3131},[611,697],[568,3133,1207],{"className":3134},[1206],[568,3136,3138],{"className":3137},[677],[568,3139,3141],{"className":3140,"style":3085},[681],[568,3142],{},[564,3144,3145,3320,3321,3349,3350,988],{},[568,3146,3148,3194],{"className":3147},[571],[568,3149,3151],{"className":3150},[575],[577,3152,3153],{"xmlns":579},[581,3154,3155,3191],{},[584,3156,3157,3159,3189],{},[642,3158,1623],{"fence":598},[1625,3160,3161,3175],{"rowspacing":1627,"columnalign":1628,"columnspacing":1629},[1631,3162,3163,3169],{},[1634,3164,3165],{},[1637,3166,3167],{"scriptlevel":1639,"displaystyle":1034},[782,3168,784],{},[1634,3170,3171],{},[1637,3172,3173],{"scriptlevel":1639,"displaystyle":1034},[782,3174,784],{},[1631,3176,3177,3183],{},[1634,3178,3179],{},[1637,3180,3181],{"scriptlevel":1639,"displaystyle":1034},[782,3182,1639],{},[1634,3184,3185],{},[1637,3186,3187],{"scriptlevel":1639,"displaystyle":1034},[782,3188,784],{},[642,3190,1670],{"fence":598},[591,3192,3193],{"encoding":593},"\\begin{pmatrix} 1 & 1 \\\\ 0 & 1 \\end{pmatrix}",[568,3195,3197],{"className":3196,"ariaHidden":598},[597],[568,3198,3200,3203],{"className":3199},[602],[568,3201],{"className":3202,"style":1701},[606],[568,3204,3206,3212,3314],{"className":3205},[1784],[568,3207,3209],{"className":3208,"style":1789},[1098,1788],[568,3210,1623],{"className":3211},[1793,696],[568,3213,3215],{"className":3214},[611],[568,3216,3218,3263,3266,3269],{"className":3217},[1625],[568,3219,3221],{"className":3220},[1803],[568,3222,3224,3255],{"className":3223},[673,1171],[568,3225,3227,3252],{"className":3226},[677],[568,3228,3230,3241],{"className":3229,"style":1813},[681],[568,3231,3232,3235],{"style":1816},[568,3233],{"className":3234,"style":1122},[689],[568,3236,3238],{"className":3237},[611],[568,3239,784],{"className":3240},[611],[568,3242,3243,3246],{"style":1828},[568,3244],{"className":3245,"style":1122},[689],[568,3247,3249],{"className":3248},[611],[568,3250,1639],{"className":3251},[611],[568,3253,1207],{"className":3254},[1206],[568,3256,3258],{"className":3257},[677],[568,3259,3261],{"className":3260,"style":1847},[681],[568,3262],{},[568,3264],{"className":3265,"style":1854},[1853],[568,3267],{"className":3268,"style":1854},[1853],[568,3270,3272],{"className":3271},[1803],[568,3273,3275,3306],{"className":3274},[673,1171],[568,3276,3278,3303],{"className":3277},[677],[568,3279,3281,3292],{"className":3280,"style":1813},[681],[568,3282,3283,3286],{"style":1816},[568,3284],{"className":3285,"style":1122},[689],[568,3287,3289],{"className":3288},[611],[568,3290,784],{"className":3291},[611],[568,3293,3294,3297],{"style":1828},[568,3295],{"className":3296,"style":1122},[689],[568,3298,3300],{"className":3299},[611],[568,3301,784],{"className":3302},[611],[568,3304,1207],{"className":3305},[1206],[568,3307,3309],{"className":3308},[677],[568,3310,3312],{"className":3311,"style":1847},[681],[568,3313],{},[568,3315,3317],{"className":3316,"style":1789},[1220,1788],[568,3318,1670],{"className":3319},[1793,696]," ist nicht orthogonal: Die erste Spalte hat zwar Länge ",[568,3322,3324,3337],{"className":3323},[571],[568,3325,3327],{"className":3326},[575],[577,3328,3329],{"xmlns":579},[581,3330,3331,3335],{},[584,3332,3333],{},[782,3334,784],{},[591,3336,784],{"encoding":593},[568,3338,3340],{"className":3339,"ariaHidden":598},[597],[568,3341,3343,3346],{"className":3342},[602],[568,3344],{"className":3345,"style":796},[606],[568,3347,784],{"className":3348},[611],", aber das Skalarprodukt der Spalten ist ",[568,3351,3353,3373],{"className":3352},[571],[568,3354,3356],{"className":3355},[575],[577,3357,3358],{"xmlns":579},[581,3359,3360,3370],{},[584,3361,3362,3364,3368],{},[782,3363,784],{},[642,3365,3367],{"mathvariant":3366},"normal","≠",[782,3369,1639],{},[591,3371,3372],{"encoding":593},"1 \\neq 0",[568,3374,3376,3434],{"className":3375,"ariaHidden":598},[597],[568,3377,3379,3382,3385,3388,3431],{"className":3378},[602],[568,3380],{"className":3381,"style":1376},[606],[568,3383,784],{"className":3384},[611],[568,3386],{"className":3387,"style":709},[708],[568,3389,3391,3424,3428],{"className":3390},[713],[568,3392,3394],{"className":3393},[713],[568,3395,3398],{"className":3396},[611,3397],"vbox",[568,3399,3402],{"className":3400},[3401],"thinbox",[568,3403,3406,3409,3420],{"className":3404},[3405],"rlap",[568,3407],{"className":3408,"style":1376},[606],[568,3410,3413],{"className":3411},[3412],"inner",[568,3414,3416],{"className":3415},[611],[568,3417,3419],{"className":3418},[713],"",[568,3421],{"className":3422},[3423],"fix",[568,3425],{"className":3426},[708,3427],"nobreak",[568,3429,644],{"className":3430},[713],[568,3432],{"className":3433,"style":709},[708],[568,3435,3437,3440],{"className":3436},[602],[568,3438],{"className":3439,"style":796},[606],[568,3441,1639],{"className":3442},[611],[559,3444,3446],{"id":3445},"typische-fehler","Typische Fehler",[730,3448,3449,3657,3929],{},[733,3450,3451,3452,3480,3481,3656],{},"Nur prüfen, ob die Spalten senkrecht aufeinander stehen. Sie müssen außerdem die Länge ",[568,3453,3455,3468],{"className":3454},[571],[568,3456,3458],{"className":3457},[575],[577,3459,3460],{"xmlns":579},[581,3461,3462,3466],{},[584,3463,3464],{},[782,3465,784],{},[591,3467,784],{"encoding":593},[568,3469,3471],{"className":3470,"ariaHidden":598},[597],[568,3472,3474,3477],{"className":3473},[602],[568,3475],{"className":3476,"style":796},[606],[568,3478,784],{"className":3479},[611]," haben. ",[568,3482,3484,3530],{"className":3483},[571],[568,3485,3487],{"className":3486},[575],[577,3488,3489],{"xmlns":579},[581,3490,3491,3527],{},[584,3492,3493,3495,3525],{},[642,3494,1623],{"fence":598},[1625,3496,3497,3511],{"rowspacing":1627,"columnalign":1628,"columnspacing":1629},[1631,3498,3499,3505],{},[1634,3500,3501],{},[1637,3502,3503],{"scriptlevel":1639,"displaystyle":1034},[782,3504,3031],{},[1634,3506,3507],{},[1637,3508,3509],{"scriptlevel":1639,"displaystyle":1034},[782,3510,1639],{},[1631,3512,3513,3519],{},[1634,3514,3515],{},[1637,3516,3517],{"scriptlevel":1639,"displaystyle":1034},[782,3518,1639],{},[1634,3520,3521],{},[1637,3522,3523],{"scriptlevel":1639,"displaystyle":1034},[782,3524,3031],{},[642,3526,1670],{"fence":598},[591,3528,3529],{"encoding":593},"\\begin{pmatrix} 2 & 0 \\\\ 0 & 2 \\end{pmatrix}",[568,3531,3533],{"className":3532,"ariaHidden":598},[597],[568,3534,3536,3539],{"className":3535},[602],[568,3537],{"className":3538,"style":1701},[606],[568,3540,3542,3548,3650],{"className":3541},[1784],[568,3543,3545],{"className":3544,"style":1789},[1098,1788],[568,3546,1623],{"className":3547},[1793,696],[568,3549,3551],{"className":3550},[611],[568,3552,3554,3599,3602,3605],{"className":3553},[1625],[568,3555,3557],{"className":3556},[1803],[568,3558,3560,3591],{"className":3559},[673,1171],[568,3561,3563,3588],{"className":3562},[677],[568,3564,3566,3577],{"className":3565,"style":1813},[681],[568,3567,3568,3571],{"style":1816},[568,3569],{"className":3570,"style":1122},[689],[568,3572,3574],{"className":3573},[611],[568,3575,3031],{"className":3576},[611],[568,3578,3579,3582],{"style":1828},[568,3580],{"className":3581,"style":1122},[689],[568,3583,3585],{"className":3584},[611],[568,3586,1639],{"className":3587},[611],[568,3589,1207],{"className":3590},[1206],[568,3592,3594],{"className":3593},[677],[568,3595,3597],{"className":3596,"style":1847},[681],[568,3598],{},[568,3600],{"className":3601,"style":1854},[1853],[568,3603],{"className":3604,"style":1854},[1853],[568,3606,3608],{"className":3607},[1803],[568,3609,3611,3642],{"className":3610},[673,1171],[568,3612,3614,3639],{"className":3613},[677],[568,3615,3617,3628],{"className":3616,"style":1813},[681],[568,3618,3619,3622],{"style":1816},[568,3620],{"className":3621,"style":1122},[689],[568,3623,3625],{"className":3624},[611],[568,3626,1639],{"className":3627},[611],[568,3629,3630,3633],{"style":1828},[568,3631],{"className":3632,"style":1122},[689],[568,3634,3636],{"className":3635},[611],[568,3637,3031],{"className":3638},[611],[568,3640,1207],{"className":3641},[1206],[568,3643,3645],{"className":3644},[677],[568,3646,3648],{"className":3647,"style":1847},[681],[568,3649],{},[568,3651,3653],{"className":3652,"style":1789},[1220,1788],[568,3654,1670],{"className":3655},[1793,696]," hat orthogonale Spalten, ist aber nicht orthogonal.",[733,3658,3659,3660,3725,3726,3900,3901,988],{},"Aus ",[568,3661,3663,3686],{"className":3662},[571],[568,3664,3666],{"className":3665},[575],[577,3667,3668],{"xmlns":579},[581,3669,3670,3684],{},[584,3671,3672,3674,3676,3678,3680,3682],{},[587,3673,1351],{},[642,3675,1354],{},[587,3677,589],{},[642,3679,644],{},[642,3681,1361],{},[782,3683,784],{},[591,3685,1366],{"encoding":593},[568,3687,3689,3713],{"className":3688,"ariaHidden":598},[597],[568,3690,3692,3695,3698,3701,3704,3707,3710],{"className":3691},[602],[568,3693],{"className":3694,"style":1376},[606],[568,3696,1351],{"className":3697},[1380],[568,3699],{"className":3700,"style":1161},[708],[568,3702,589],{"className":3703},[611,612],[568,3705],{"className":3706,"style":709},[708],[568,3708,644],{"className":3709},[713],[568,3711],{"className":3712,"style":709},[708],[568,3714,3716,3719,3722],{"className":3715},[602],[568,3717],{"className":3718,"style":1402},[606],[568,3720,1361],{"className":3721},[611],[568,3723,784],{"className":3724},[611]," auf Orthogonalität schließen. Die Umkehrung gilt nicht, z.B. hat ",[568,3727,3729,3774],{"className":3728},[571],[568,3730,3732],{"className":3731},[575],[577,3733,3734],{"xmlns":579},[581,3735,3736,3772],{},[584,3737,3738,3740,3770],{},[642,3739,1623],{"fence":598},[1625,3741,3742,3756],{"rowspacing":1627,"columnalign":1628,"columnspacing":1629},[1631,3743,3744,3750],{},[1634,3745,3746],{},[1637,3747,3748],{"scriptlevel":1639,"displaystyle":1034},[782,3749,784],{},[1634,3751,3752],{},[1637,3753,3754],{"scriptlevel":1639,"displaystyle":1034},[782,3755,784],{},[1631,3757,3758,3764],{},[1634,3759,3760],{},[1637,3761,3762],{"scriptlevel":1639,"displaystyle":1034},[782,3763,1639],{},[1634,3765,3766],{},[1637,3767,3768],{"scriptlevel":1639,"displaystyle":1034},[782,3769,784],{},[642,3771,1670],{"fence":598},[591,3773,3193],{"encoding":593},[568,3775,3777],{"className":3776,"ariaHidden":598},[597],[568,3778,3780,3783],{"className":3779},[602],[568,3781],{"className":3782,"style":1701},[606],[568,3784,3786,3792,3894],{"className":3785},[1784],[568,3787,3789],{"className":3788,"style":1789},[1098,1788],[568,3790,1623],{"className":3791},[1793,696],[568,3793,3795],{"className":3794},[611],[568,3796,3798,3843,3846,3849],{"className":3797},[1625],[568,3799,3801],{"className":3800},[1803],[568,3802,3804,3835],{"className":3803},[673,1171],[568,3805,3807,3832],{"className":3806},[677],[568,3808,3810,3821],{"className":3809,"style":1813},[681],[568,3811,3812,3815],{"style":1816},[568,3813],{"className":3814,"style":1122},[689],[568,3816,3818],{"className":3817},[611],[568,3819,784],{"className":3820},[611],[568,3822,3823,3826],{"style":1828},[568,3824],{"className":3825,"style":1122},[689],[568,3827,3829],{"className":3828},[611],[568,3830,1639],{"className":3831},[611],[568,3833,1207],{"className":3834},[1206],[568,3836,3838],{"className":3837},[677],[568,3839,3841],{"className":3840,"style":1847},[681],[568,3842],{},[568,3844],{"className":3845,"style":1854},[1853],[568,3847],{"className":3848,"style":1854},[1853],[568,3850,3852],{"className":3851},[1803],[568,3853,3855,3886],{"className":3854},[673,1171],[568,3856,3858,3883],{"className":3857},[677],[568,3859,3861,3872],{"className":3860,"style":1813},[681],[568,3862,3863,3866],{"style":1816},[568,3864],{"className":3865,"style":1122},[689],[568,3867,3869],{"className":3868},[611],[568,3870,784],{"className":3871},[611],[568,3873,3874,3877],{"style":1828},[568,3875],{"className":3876,"style":1122},[689],[568,3878,3880],{"className":3879},[611],[568,3881,784],{"className":3882},[611],[568,3884,1207],{"className":3885},[1206],[568,3887,3889],{"className":3888},[677],[568,3890,3892],{"className":3891,"style":1847},[681],[568,3893],{},[568,3895,3897],{"className":3896,"style":1789},[1220,1788],[568,3898,1670],{"className":3899},[1793,696]," Determinante ",[568,3902,3904,3917],{"className":3903},[571],[568,3905,3907],{"className":3906},[575],[577,3908,3909],{"xmlns":579},[581,3910,3911,3915],{},[584,3912,3913],{},[782,3914,784],{},[591,3916,784],{"encoding":593},[568,3918,3920],{"className":3919,"ariaHidden":598},[597],[568,3921,3923,3926],{"className":3922},[602],[568,3924],{"className":3925,"style":796},[606],[568,3927,784],{"className":3928},[611],[733,3930,3931,4000,4001,4060],{},[568,3932,3934,3956],{"className":3933},[571],[568,3935,3937],{"className":3936},[575],[577,3938,3939],{"xmlns":579},[581,3940,3941,3953],{},[584,3942,3943],{},[632,3944,3945,3947],{},[587,3946,589],{},[584,3948,3949,3951],{},[642,3950,884],{},[782,3952,784],{},[591,3954,3955],{"encoding":593},"Q^{-1}",[568,3957,3959],{"className":3958,"ariaHidden":598},[597],[568,3960,3962,3965],{"className":3961},[602],[568,3963],{"className":3964,"style":907},[606],[568,3966,3968,3971],{"className":3967},[611],[568,3969,589],{"className":3970},[611,612],[568,3972,3974],{"className":3973},[669],[568,3975,3977],{"className":3976},[673],[568,3978,3980],{"className":3979},[677],[568,3981,3983],{"className":3982,"style":926},[681],[568,3984,3985,3988],{"style":685},[568,3986],{"className":3987,"style":690},[689],[568,3989,3991],{"className":3990},[694,695,696,697],[568,3992,3994,3997],{"className":3993},[611,697],[568,3995,884],{"className":3996},[611,697],[568,3998,784],{"className":3999},[611,697]," aufwendig berechnen, obwohl ",[568,4002,4004,4022],{"className":4003},[571],[568,4005,4007],{"className":4006},[575],[577,4008,4009],{"xmlns":579},[581,4010,4011,4019],{},[584,4012,4013],{},[632,4014,4015,4017],{},[587,4016,589],{},[587,4018,638],{},[591,4020,4021],{"encoding":593},"Q^T",[568,4023,4025],{"className":4024,"ariaHidden":598},[597],[568,4026,4028,4031],{"className":4027},[602],[568,4029],{"className":4030,"style":659},[606],[568,4032,4034,4037],{"className":4033},[611],[568,4035,589],{"className":4036},[611,612],[568,4038,4040],{"className":4039},[669],[568,4041,4043],{"className":4042},[673],[568,4044,4046],{"className":4045},[677],[568,4047,4049],{"className":4048,"style":682},[681],[568,4050,4051,4054],{"style":685},[568,4052],{"className":4053,"style":690},[689],[568,4055,4057],{"className":4056},[694,695,696,697],[568,4058,638],{"className":4059,"style":701},[611,612,697]," genügt.",{"title":4062,"searchDepth":4063,"depth":4063,"links":4064},"",2,[4065,4066,4067],{"id":561,"depth":4063,"text":562},{"id":1591,"depth":4063,"text":1592},{"id":3445,"depth":4063,"text":3446},[4069,4071,4073,4076,4078,4080,4082,4084,4086,4088,4090,4092,4094],{"lhs":4070,"rhs":784},"multiply(transpose([[cos(x), -sin(x)], [sin(x), cos(x)]]), [[cos(x), -sin(x)], [sin(x), cos(x)]])[1, 1]",{"lhs":4072,"rhs":1639},"multiply(transpose([[cos(x), -sin(x)], [sin(x), cos(x)]]), [[cos(x), -sin(x)], [sin(x), cos(x)]])[1, 2]",{"lhs":4074,"rhs":4075},"norm(multiply([[cos(x), -sin(x)], [sin(x), cos(x)]], [p, q]))","sqrt(p^2 + q^2)",{"lhs":4077,"rhs":784},"0.6^2 + 0.8^2",{"lhs":4079,"rhs":1639},"0.6*(-0.8) + 0.8*0.6",{"lhs":4081,"rhs":784},"det([[0.6, -0.8], [0.8, 0.6]])",{"lhs":4083,"rhs":1642},"multiply([[0.6, -0.8], [0.8, 0.6]], [5, 0])[1]",{"lhs":4085,"rhs":1653},"multiply([[0.6, -0.8], [0.8, 0.6]], [5, 0])[2]",{"lhs":4087,"rhs":1618},"norm([3, 4])",{"lhs":4089,"rhs":1497},"det([[0, 1, 0], [1, 0, 0], [0, 0, 1]])",{"lhs":4091,"rhs":784},"multiply(transpose([[0, 1, 0], [1, 0, 0], [0, 0, 1]]), [[0, 1, 0], [1, 0, 0], [0, 0, 1]])[1, 1]",{"lhs":4093,"rhs":784},"1^2 + 0^2",{"lhs":4095,"rhs":784},"1*1 + 0*1","Q \\in \\mathbb{R}^{n \\times n}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>Q\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">Q \\in \\mathbb{R}^{n \\times n}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">Q\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7713em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","orthogonal-matrix","Q^{T} Q = Q Q^{T} = E \\quad\\Longleftrightarrow\\quad Q^{-1} = Q^{T}","\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>\u003Cmsup>\u003Cmi>Q\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmi>Q\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>Q\u003C\u002Fmi>\u003Cmsup>\u003Cmi>Q\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>E\u003C\u002Fmi>\u003Cmspace width=\"1em\"\u002F>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmsup>\u003Cmi>Q\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>Q\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">Q^{T} Q = Q Q^{T} = E \\quad\\Longleftrightarrow\\quad Q^{-1} = Q^{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:1.0858em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">Q\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 mathnormal\">Q\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:1.0858em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">Q\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">Q\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:0.7073em;vertical-align:-0.024em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⟺\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0585em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">Q\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"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:1.0858em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">Q\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Forthogonale-matrix",[],[4109,4110,4111,4112],"rotation-matrix","transpose-rules","gram-schmidt","determinant-rules",{"title":548,"description":4062},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Forthogonale-matrix","Eine Matrix ist orthogonal, wenn ihre Spalten eine Orthonormalbasis bilden; dann ist ihre Inverse die Transponierte.",[4117,4118,4119,4120,4121],"orthogonale matrix","orthonormalbasis","transponierte","drehung","spiegelung",[4123,4126,4130],{"symbol":589,"meaning":4124,"symbolHtml":4125},"quadratische reelle Matrix","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>Q\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">Q\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\">Q\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4127,"meaning":4128,"symbolHtml":4129},"Q^{T}","Transponierte von Q","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>Q\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">Q^{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:1.0358em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">Q\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>",{"symbol":647,"meaning":4131,"symbolHtml":4132},"n × n-Einheitsmatrix","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E\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\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","rwJ2hAnAxc4dJhYcfc8TI35SqOFl43rRjWQrP0SSMHI",[4135,4138,4141,4144],{"stem":4136,"title":4137,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fdrehmatrix","Drehmatrix in der Ebene",{"stem":4139,"title":4140,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fgram-schmidt-verfahren","Gram-Schmidt-Verfahren",{"stem":4142,"title":4143,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Frechenregeln-determinanten","Rechenregeln für Determinanten",{"stem":4145,"title":4146,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Frechenregeln-transponierte","Rechenregeln für die Transponierte",1793824279283]