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",[574,1584,1586,1626],{"className":1585},[577],[574,1587,1589],{"className":1588},[581],[583,1590,1591],{"xmlns":585},[587,1592,1593,1623],{},[590,1594,1595,1601,1603,1605,1609,1611,1617],{},[608,1596,1597,1599],{"accent":610},[593,1598,914],{},[597,1600,616],{},[597,1602,599],{},[593,1604,1566],{},[1606,1607,1608],"mtext",{}," ",[597,1610,909],{"stretchy":602},[608,1612,1613,1615],{"accent":610},[593,1614,914],{},[597,1616,616],{},[605,1618,1619,1621],{},[597,1620,921],{"stretchy":602},[593,1622,595],{},[644,1624,1625],{"encoding":646},"\\vec v = S\\,[\\vec v]_B",[574,1627,1629,1679],{"className":1628,"ariaHidden":610},[651],[574,1630,1632,1635,1670,1673,1676],{"className":1631},[655],[574,1633],{"className":1634,"style":977},[659],[574,1636,1638],{"className":1637},[664,696],[574,1639,1641],{"className":1640},[700],[574,1642,1644],{"className":1643},[704],[574,1645,1647,1655],{"className":1646,"style":977},[708],[574,1648,1649,1652],{"style":712},[574,1650],{"className":1651,"style":717},[716],[574,1653,914],{"className":1654,"style":986},[664,665],[574,1656,1657,1660],{"style":712},[574,1658],{"className":1659,"style":717},[716],[574,1661,1663],{"className":1662,"style":995},[730],[574,1664,1666],{"className":1665,"style":736},[735],[738,1667,1668],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,1669],{"d":749},[574,1671],{"className":1672,"style":671},[670],[574,1674,599],{"className":1675},[675],[574,1677],{"className":1678,"style":671},[670],[574,1680,1682,1685,1688,1691,1694,1729],{"className":1681},[655],[574,1683],{"className":1684,"style":961},[659],[574,1686,1566],{"className":1687,"style":1581},[664,665],[574,1689],{"className":1690,"style":803},[670],[574,1692,909],{"className":1693},[689],[574,1695,1697],{"className":1696},[664,696],[574,1698,1700],{"className":1699},[700],[574,1701,1703],{"className":1702},[704],[574,1704,1706,1714],{"className":1705,"style":977},[708],[574,1707,1708,1711],{"style":712},[574,1709],{"className":1710,"style":717},[716],[574,1712,914],{"className":1713,"style":986},[664,665],[574,1715,1716,1719],{"style":712},[574,1717],{"className":1718,"style":717},[716],[574,1720,1722],{"className":1721,"style":995},[730],[574,1723,1725],{"className":1724,"style":736},[735],[738,1726,1727],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,1728],{"d":749},[574,1730,1732,1735],{"className":1731},[893],[574,1733,921],{"className":1734},[893],[574,1736,1738],{"className":1737},[753],[574,1739,1741,1761],{"className":1740},[700,757],[574,1742,1744,1758],{"className":1743},[704],[574,1745,1747],{"className":1746,"style":1021},[708],[574,1748,1749,1752],{"style":767},[574,1750],{"className":1751,"style":771},[716],[574,1753,1755],{"className":1754},[775,776,777,778],[574,1756,595],{"className":1757,"style":666},[664,665,778],[574,1759,786],{"className":1760},[785],[574,1762,1764],{"className":1763},[704],[574,1765,1767],{"className":1766,"style":793},[708],[574,1768],{},". Daraus folgt:",[1771,1772,1773,2131],"ul",{},[1774,1775,1776,572,1779,2002,2003,2031,2032,2060,2061,2130],"li",{},[569,1777,1778],{},"Koordinaten umrechnen:",[574,1780,1782,1828],{"className":1781},[577],[574,1783,1785],{"className":1784},[581],[583,1786,1787],{"xmlns":585},[587,1788,1789,1825],{},[590,1790,1791,1793,1799,1805,1807,1819],{},[597,1792,909],{"stretchy":602},[608,1794,1795,1797],{"accent":610},[593,1796,914],{},[597,1798,616],{},[605,1800,1801,1803],{},[597,1802,921],{"stretchy":602},[593,1804,595],{},[597,1806,599],{},[1808,1809,1810,1812],"msup",{},[593,1811,1566],{},[590,1813,1814,1817],{},[597,1815,1816],{},"−",[618,1818,620],{},[608,1820,1821,1823],{"accent":610},[593,1822,914],{},[597,1824,616],{},[644,1826,1827],{"encoding":646},"[\\vec v]_B = S^{-1}\\vec v",[574,1829,1831,1924],{"className":1830,"ariaHidden":610},[651],[574,1832,1834,1837,1840,1875,1915,1918,1921],{"className":1833},[655],[574,1835],{"className":1836,"style":961},[659],[574,1838,909],{"className":1839},[689],[574,1841,1843],{"className":1842},[664,696],[574,1844,1846],{"className":1845},[700],[574,1847,1849],{"className":1848},[704],[574,1850,1852,1860],{"className":1851,"style":977},[708],[574,1853,1854,1857],{"style":712},[574,1855],{"className":1856,"style":717},[716],[574,1858,914],{"className":1859,"style":986},[664,665],[574,1861,1862,1865],{"style":712},[574,1863],{"className":1864,"style":717},[716],[574,1866,1868],{"className":1867,"style":995},[730],[574,1869,1871],{"className":1870,"style":736},[735],[738,1872,1873],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,1874],{"d":749},[574,1876,1878,1881],{"className":1877},[893],[574,1879,921],{"className":1880},[893],[574,1882,1884],{"className":1883},[753],[574,1885,1887,1907],{"className":1886},[700,757],[574,1888,1890,1904],{"className":1889},[704],[574,1891,1893],{"className":1892,"style":1021},[708],[574,1894,1895,1898],{"style":767},[574,1896],{"className":1897,"style":771},[716],[574,1899,1901],{"className":1900},[775,776,777,778],[574,1902,595],{"className":1903,"style":666},[664,665,778],[574,1905,786],{"className":1906},[785],[574,1908,1910],{"className":1909},[704],[574,1911,1913],{"className":1912,"style":793},[708],[574,1914],{},[574,1916],{"className":1917,"style":671},[670],[574,1919,599],{"className":1920},[675],[574,1922],{"className":1923,"style":671},[670],[574,1925,1927,1931,1967],{"className":1926},[655],[574,1928],{"className":1929,"style":1930},[659],"height:0.8141em;",[574,1932,1934,1937],{"className":1933},[664],[574,1935,1566],{"className":1936,"style":1581},[664,665],[574,1938,1940],{"className":1939},[753],[574,1941,1943],{"className":1942},[700],[574,1944,1946],{"className":1945},[704],[574,1947,1949],{"className":1948,"style":1930},[708],[574,1950,1952,1955],{"style":1951},"top:-3.063em;margin-right:0.05em;",[574,1953],{"className":1954,"style":771},[716],[574,1956,1958],{"className":1957},[775,776,777,778],[574,1959,1961,1964],{"className":1960},[664,778],[574,1962,1816],{"className":1963},[664,778],[574,1965,620],{"className":1966},[664,778],[574,1968,1970],{"className":1969},[664,696],[574,1971,1973],{"className":1972},[700],[574,1974,1976],{"className":1975},[704],[574,1977,1979,1987],{"className":1978,"style":977},[708],[574,1980,1981,1984],{"style":712},[574,1982],{"className":1983,"style":717},[716],[574,1985,914],{"className":1986,"style":986},[664,665],[574,1988,1989,1992],{"style":712},[574,1990],{"className":1991,"style":717},[716],[574,1993,1995],{"className":1994,"style":995},[730],[574,1996,1998],{"className":1997,"style":736},[735],[738,1999,2000],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,2001],{"d":749},". Die Richtung merkt man sich so: ",[574,2004,2006,2019],{"className":2005},[577],[574,2007,2009],{"className":2008},[581],[583,2010,2011],{"xmlns":585},[587,2012,2013,2017],{},[590,2014,2015],{},[593,2016,1566],{},[644,2018,1566],{"encoding":646},[574,2020,2022],{"className":2021,"ariaHidden":610},[651],[574,2023,2025,2028],{"className":2024},[655],[574,2026],{"className":2027,"style":660},[659],[574,2029,1566],{"className":2030,"style":1581},[664,665]," übersetzt von ",[574,2033,2035,2048],{"className":2034},[577],[574,2036,2038],{"className":2037},[581],[583,2039,2040],{"xmlns":585},[587,2041,2042,2046],{},[590,2043,2044],{},[593,2045,595],{},[644,2047,595],{"encoding":646},[574,2049,2051],{"className":2050,"ariaHidden":610},[651],[574,2052,2054,2057],{"className":2053},[655],[574,2055],{"className":2056,"style":660},[659],[574,2058,595],{"className":2059,"style":666},[664,665],"-Koordinaten in Standardkoordinaten, ",[574,2062,2064,2086],{"className":2063},[577],[574,2065,2067],{"className":2066},[581],[583,2068,2069],{"xmlns":585},[587,2070,2071,2083],{},[590,2072,2073],{},[1808,2074,2075,2077],{},[593,2076,1566],{},[590,2078,2079,2081],{},[597,2080,1816],{},[618,2082,620],{},[644,2084,2085],{"encoding":646},"S^{-1}",[574,2087,2089],{"className":2088,"ariaHidden":610},[651],[574,2090,2092,2095],{"className":2091},[655],[574,2093],{"className":2094,"style":1930},[659],[574,2096,2098,2101],{"className":2097},[664],[574,2099,1566],{"className":2100,"style":1581},[664,665],[574,2102,2104],{"className":2103},[753],[574,2105,2107],{"className":2106},[700],[574,2108,2110],{"className":2109},[704],[574,2111,2113],{"className":2112,"style":1930},[708],[574,2114,2115,2118],{"style":1951},[574,2116],{"className":2117,"style":771},[716],[574,2119,2121],{"className":2120},[775,776,777,778],[574,2122,2124,2127],{"className":2123},[664,778],[574,2125,1816],{"className":2126},[664,778],[574,2128,620],{"className":2129},[664,778]," zurück.",[1774,2132,2133,2136,2137,2166,2167,2195,2196,2339,2340,2368,2369,2397,2398,2426,2427,2495],{},[569,2134,2135],{},"Abbildungsmatrix umrechnen:"," Hat eine lineare Abbildung in Standardkoordinaten die Matrix ",[574,2138,2140,2154],{"className":2139},[577],[574,2141,2143],{"className":2142},[581],[583,2144,2145],{"xmlns":585},[587,2146,2147,2152],{},[590,2148,2149],{},[593,2150,2151],{},"A",[644,2153,2151],{"encoding":646},[574,2155,2157],{"className":2156,"ariaHidden":610},[651],[574,2158,2160,2163],{"className":2159},[655],[574,2161],{"className":2162,"style":660},[659],[574,2164,2151],{"className":2165},[664,665],", dann hat sie in ",[574,2168,2170,2183],{"className":2169},[577],[574,2171,2173],{"className":2172},[581],[583,2174,2175],{"xmlns":585},[587,2176,2177,2181],{},[590,2178,2179],{},[593,2180,595],{},[644,2182,595],{"encoding":646},[574,2184,2186],{"className":2185,"ariaHidden":610},[651],[574,2187,2189,2192],{"className":2188},[655],[574,2190],{"className":2191,"style":660},[659],[574,2193,595],{"className":2194,"style":666},[664,665],"-Koordinaten die Matrix ",[574,2197,2199,2233],{"className":2198},[577],[574,2200,2202],{"className":2201},[581],[583,2203,2204],{"xmlns":585},[587,2205,2206,2230],{},[590,2207,2208,2214,2216,2226,2228],{},[605,2209,2210,2212],{},[593,2211,2151],{},[593,2213,595],{},[597,2215,599],{},[1808,2217,2218,2220],{},[593,2219,1566],{},[590,2221,2222,2224],{},[597,2223,1816],{},[618,2225,620],{},[593,2227,2151],{},[593,2229,1566],{},[644,2231,2232],{"encoding":646},"A_B = S^{-1} A S",[574,2234,2236,2292],{"className":2235,"ariaHidden":610},[651],[574,2237,2239,2243,2283,2286,2289],{"className":2238},[655],[574,2240],{"className":2241,"style":2242},[659],"height:0.8333em;vertical-align:-0.15em;",[574,2244,2246,2249],{"className":2245},[664],[574,2247,2151],{"className":2248},[664,665],[574,2250,2252],{"className":2251},[753],[574,2253,2255,2275],{"className":2254},[700,757],[574,2256,2258,2272],{"className":2257},[704],[574,2259,2261],{"className":2260,"style":1021},[708],[574,2262,2263,2266],{"style":767},[574,2264],{"className":2265,"style":771},[716],[574,2267,2269],{"className":2268},[775,776,777,778],[574,2270,595],{"className":2271,"style":666},[664,665,778],[574,2273,786],{"className":2274},[785],[574,2276,2278],{"className":2277},[704],[574,2279,2281],{"className":2280,"style":793},[708],[574,2282],{},[574,2284],{"className":2285,"style":671},[670],[574,2287,599],{"className":2288},[675],[574,2290],{"className":2291,"style":671},[670],[574,2293,2295,2298,2333,2336],{"className":2294},[655],[574,2296],{"className":2297,"style":1930},[659],[574,2299,2301,2304],{"className":2300},[664],[574,2302,1566],{"className":2303,"style":1581},[664,665],[574,2305,2307],{"className":2306},[753],[574,2308,2310],{"className":2309},[700],[574,2311,2313],{"className":2312},[704],[574,2314,2316],{"className":2315,"style":1930},[708],[574,2317,2318,2321],{"style":1951},[574,2319],{"className":2320,"style":771},[716],[574,2322,2324],{"className":2323},[775,776,777,778],[574,2325,2327,2330],{"className":2326},[664,778],[574,2328,1816],{"className":2329},[664,778],[574,2331,620],{"className":2332},[664,778],[574,2334,2151],{"className":2335},[664,665],[574,2337,1566],{"className":2338,"style":1581},[664,665],". Gelesen von rechts: ",[574,2341,2343,2356],{"className":2342},[577],[574,2344,2346],{"className":2345},[581],[583,2347,2348],{"xmlns":585},[587,2349,2350,2354],{},[590,2351,2352],{},[593,2353,595],{},[644,2355,595],{"encoding":646},[574,2357,2359],{"className":2358,"ariaHidden":610},[651],[574,2360,2362,2365],{"className":2361},[655],[574,2363],{"className":2364,"style":660},[659],[574,2366,595],{"className":2367,"style":666},[664,665],"-Koordinaten in Standardkoordinaten übersetzen (",[574,2370,2372,2385],{"className":2371},[577],[574,2373,2375],{"className":2374},[581],[583,2376,2377],{"xmlns":585},[587,2378,2379,2383],{},[590,2380,2381],{},[593,2382,1566],{},[644,2384,1566],{"encoding":646},[574,2386,2388],{"className":2387,"ariaHidden":610},[651],[574,2389,2391,2394],{"className":2390},[655],[574,2392],{"className":2393,"style":660},[659],[574,2395,1566],{"className":2396,"style":1581},[664,665],"), abbilden (",[574,2399,2401,2414],{"className":2400},[577],[574,2402,2404],{"className":2403},[581],[583,2405,2406],{"xmlns":585},[587,2407,2408,2412],{},[590,2409,2410],{},[593,2411,2151],{},[644,2413,2151],{"encoding":646},[574,2415,2417],{"className":2416,"ariaHidden":610},[651],[574,2418,2420,2423],{"className":2419},[655],[574,2421],{"className":2422,"style":660},[659],[574,2424,2151],{"className":2425},[664,665],"), zurückübersetzen (",[574,2428,2430,2451],{"className":2429},[577],[574,2431,2433],{"className":2432},[581],[583,2434,2435],{"xmlns":585},[587,2436,2437,2449],{},[590,2438,2439],{},[1808,2440,2441,2443],{},[593,2442,1566],{},[590,2444,2445,2447],{},[597,2446,1816],{},[618,2448,620],{},[644,2450,2085],{"encoding":646},[574,2452,2454],{"className":2453,"ariaHidden":610},[651],[574,2455,2457,2460],{"className":2456},[655],[574,2458],{"className":2459,"style":1930},[659],[574,2461,2463,2466],{"className":2462},[664],[574,2464,1566],{"className":2465,"style":1581},[664,665],[574,2467,2469],{"className":2468},[753],[574,2470,2472],{"className":2471},[700],[574,2473,2475],{"className":2474},[704],[574,2476,2478],{"className":2477,"style":1930},[708],[574,2479,2480,2483],{"style":1951},[574,2481],{"className":2482,"style":771},[716],[574,2484,2486],{"className":2485},[775,776,777,778],[574,2487,2489,2492],{"className":2488},[664,778],[574,2490,1816],{"className":2491},[664,778],[574,2493,620],{"className":2494},[664,778],").",[565,2497,2498,2499,2578,2579,2582,2583,2611,2612,2640],{},"Matrizen der Form ",[574,2500,2502,2528],{"className":2501},[577],[574,2503,2505],{"className":2504},[581],[583,2506,2507],{"xmlns":585},[587,2508,2509,2525],{},[590,2510,2511,2521,2523],{},[1808,2512,2513,2515],{},[593,2514,1566],{},[590,2516,2517,2519],{},[597,2518,1816],{},[618,2520,620],{},[593,2522,2151],{},[593,2524,1566],{},[644,2526,2527],{"encoding":646},"S^{-1} A S",[574,2529,2531],{"className":2530,"ariaHidden":610},[651],[574,2532,2534,2537,2572,2575],{"className":2533},[655],[574,2535],{"className":2536,"style":1930},[659],[574,2538,2540,2543],{"className":2539},[664],[574,2541,1566],{"className":2542,"style":1581},[664,665],[574,2544,2546],{"className":2545},[753],[574,2547,2549],{"className":2548},[700],[574,2550,2552],{"className":2551},[704],[574,2553,2555],{"className":2554,"style":1930},[708],[574,2556,2557,2560],{"style":1951},[574,2558],{"className":2559,"style":771},[716],[574,2561,2563],{"className":2562},[775,776,777,778],[574,2564,2566,2569],{"className":2565},[664,778],[574,2567,1816],{"className":2568},[664,778],[574,2570,620],{"className":2571},[664,778],[574,2573,2151],{"className":2574},[664,665],[574,2576,1566],{"className":2577,"style":1581},[664,665]," heißen ",[569,2580,2581],{},"ähnlich"," zu ",[574,2584,2586,2599],{"className":2585},[577],[574,2587,2589],{"className":2588},[581],[583,2590,2591],{"xmlns":585},[587,2592,2593,2597],{},[590,2594,2595],{},[593,2596,2151],{},[644,2598,2151],{"encoding":646},[574,2600,2602],{"className":2601,"ariaHidden":610},[651],[574,2603,2605,2608],{"className":2604},[655],[574,2606],{"className":2607,"style":660},[659],[574,2609,2151],{"className":2610},[664,665],". Sie beschreiben dieselbe Abbildung in einer anderen Basis und haben dieselbe Spur, Determinante, denselben Rang und dieselben Eigenwerte. Die Diagonalisierung ist der Spezialfall, in dem ",[574,2613,2615,2628],{"className":2614},[577],[574,2616,2618],{"className":2617},[581],[583,2619,2620],{"xmlns":585},[587,2621,2622,2626],{},[590,2623,2624],{},[593,2625,595],{},[644,2627,595],{"encoding":646},[574,2629,2631],{"className":2630,"ariaHidden":610},[651],[574,2632,2634,2637],{"className":2633},[655],[574,2635],{"className":2636,"style":660},[659],[574,2638,595],{"className":2639,"style":666},[664,665]," aus Eigenvektoren besteht.",[560,2642,2644],{"id":2643},"beispiele","Beispiele",[565,2646,2647,2648,2799,2800,3024,3025,1546],{},"Basis ",[574,2649,2651,2703],{"className":2650},[577],[574,2652,2654],{"className":2653},[581],[583,2655,2656],{"xmlns":585},[587,2657,2658,2700],{},[590,2659,2660,2662,2664,2667,2669,2671,2673,2676,2678,2680,2682,2684,2686,2688,2690,2692,2694,2696,2698],{},[593,2661,595],{},[597,2663,599],{},[597,2665,603],{"fence":602,"stretchy":610,"minsize":2666,"maxsize":2666},"1.2em",[597,2668,603],{"stretchy":602},[618,2670,620],{},[597,2672,623],{"separator":610},[1606,2674,2675],{}," ",[618,2677,620],{},[597,2679,642],{"stretchy":602},[597,2681,623],{"separator":610},[1606,2683,2675],{},[597,2685,603],{"stretchy":602},[618,2687,620],{},[597,2689,623],{"separator":610},[1606,2691,2675],{},[597,2693,1816],{},[618,2695,620],{},[597,2697,642],{"stretchy":602},[597,2699,642],{"fence":602,"stretchy":610,"minsize":2666,"maxsize":2666},[644,2701,2702],{"encoding":646},"B = \\big((1,\\ 1),\\ (1,\\ 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Probe: ",[574,3749,3751,3814],{"className":3750},[577],[574,3752,3754],{"className":3753},[581],[583,3755,3756],{"xmlns":585},[587,3757,3758,3811],{},[590,3759,3760,3762,3765,3767,3769,3771,3773,3775,3777,3779,3781,3783,3785,3787,3789,3791,3793,3795,3797,3799,3801,3803,3805,3807,3809],{},[618,3761,3056],{},[597,3763,3764],{},"⋅",[597,3766,603],{"stretchy":602},[618,3768,620],{},[597,3770,623],{"separator":610},[1606,3772,2675],{},[618,3774,620],{},[597,3776,642],{"stretchy":602},[597,3778,1202],{},[618,3780,620],{},[597,3782,3764],{},[597,3784,603],{"stretchy":602},[618,3786,620],{},[597,3788,623],{"separator":610},[1606,3790,2675],{},[597,3792,1816],{},[618,3794,620],{},[597,3796,642],{"stretchy":602},[597,3798,599],{},[597,3800,603],{"stretchy":602},[618,3802,3385],{},[597,3804,623],{"separator":610},[1606,3806,2675],{},[618,3808,620],{},[597,3810,642],{"stretchy":602},[644,3812,3813],{"encoding":646},"2 \\cdot (1,\\ 1) + 1 \\cdot (1,\\ -1) = (3,\\ 1)",[574,3815,3817,3836,3872,3890,3929],{"className":3816,"ariaHidden":610},[651],[574,3818,3820,3824,3827,3830,3833],{"className":3819},[655],[574,3821],{"className":3822,"style":3823},[659],"height:0.6444em;",[574,3825,3056],{"className":3826},[664],[574,3828],{"className":3829,"style":1401},[670],[574,3831,3764],{"className":3832},[1405],[574,3834],{"className":3835,"style":1401},[670],[574,3837,3839,3842,3845,3848,3851,3854,3857,3860,3863,3866,3869],{"className":3838},[655],[574,3840],{"className":3841,"style":961},[659],[574,3843,603],{"className":3844},[689],[574,3846,620],{"className":3847},[664],[574,3849,623],{"className":3850},[799],[574,3852,2675],{"className":3853},[670],[574,3855],{"className":3856,"style":803},[670],[574,3858,620],{"className":3859},[664],[574,3861,642],{"className":3862},[893],[574,3864],{"className":3865,"style":1401},[670],[574,3867,1202],{"className":3868},[1405],[574,3870],{"className":3871,"style":1401},[670],[574,3873,3875,3878,3881,3884,3887],{"className":3874},[655],[574,3876],{"className":3877,"style":3823},[659],[574,3879,620],{"className":3880},[664],[574,3882],{"className":3883,"style":1401},[670],[574,3885,3764],{"className":3886},[1405],[574,3888],{"className":3889,"style":1401},[670],[574,3891,3893,3896,3899,3902,3905,3908,3911,3914,3917,3920,3923,3926],{"className":3892},[655],[574,3894],{"className":3895,"style":961},[659],[574,3897,603],{"className":3898},[689],[574,3900,620],{"className":3901},[664],[574,3903,623],{"className":3904},[799],[574,3906,2675],{"className":3907},[670],[574,3909],{"className":3910,"style":803},[670],[574,3912,1816],{"className":3913},[664],[574,3915,620],{"className":3916},[664],[574,3918,642],{"className":3919},[893],[574,3921],{"className":3922,"style":671},[670],[574,3924,599],{"className":3925},[675],[574,3927],{"className":3928,"style":671},[670],[574,3930,3932,3935,3938,3941,3944,3947,3950,3953],{"className":3931},[655],[574,3933],{"className":3934,"style":961},[659],[574,3936,603],{"className":3937},[689],[574,3939,3385],{"className":3940},[664],[574,3942,623],{"className":3943},[799],[574,3945,2675],{"className":3946},[670],[574,3948],{"className":3949,"style":803},[670],[574,3951,620],{"className":3952},[664],[574,3954,642],{"className":3955},[893],[565,3957,3958,3959,4158,4159,4187],{},"Die Scherung ",[574,3960,3962,4014],{"className":3961},[577],[574,3963,3965],{"className":3964},[581],[583,3966,3967],{"xmlns":585},[587,3968,3969,4011],{},[590,3970,3971,3973,3975],{},[593,3972,2151],{},[597,3974,599],{},[590,3976,3977,3979,4009],{},[597,3978,603],{"fence":610},[2821,3980,3981,3995],{"rowspacing":2823,"columnalign":2824,"columnspacing":2825},[2827,3982,3983,3989],{},[2830,3984,3985],{},[2833,3986,3987],{"scriptlevel":2835,"displaystyle":602},[618,3988,620],{},[2830,3990,3991],{},[2833,3992,3993],{"scriptlevel":2835,"displaystyle":602},[618,3994,3056],{},[2827,3996,3997,4003],{},[2830,3998,3999],{},[2833,4000,4001],{"scriptlevel":2835,"displaystyle":602},[618,4002,2835],{},[2830,4004,4005],{},[2833,4006,4007],{"scriptlevel":2835,"displaystyle":602},[618,4008,620],{},[597,4010,642],{"fence":610},[644,4012,4013],{"encoding":646},"A = \\begin{pmatrix} 1 & 2 \\\\ 0 & 1 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hat in der Basis ",[574,4160,4162,4175],{"className":4161},[577],[574,4163,4165],{"className":4164},[581],[583,4166,4167],{"xmlns":585},[587,4168,4169,4173],{},[590,4170,4171],{},[593,4172,595],{},[644,4174,595],{"encoding":646},[574,4176,4178],{"className":4177,"ariaHidden":610},[651],[574,4179,4181,4184],{"className":4180},[655],[574,4182],{"className":4183,"style":660},[659],[574,4185,595],{"className":4186,"style":666},[664,665]," die 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= S^{-1} A S = \\frac12 \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} \\begin{pmatrix} 3 & -1 \\\\ 1 & -1 \\end{pmatrix} = \\begin{pmatrix} 2 & -1 \\\\ 1 & 0 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also ist die erste Spalte von ",[574,5319,5321,5339],{"className":5320},[577],[574,5322,5324],{"className":5323},[581],[583,5325,5326],{"xmlns":585},[587,5327,5328,5336],{},[590,5329,5330],{},[605,5331,5332,5334],{},[593,5333,2151],{},[593,5335,595],{},[644,5337,5338],{"encoding":646},"A_B",[574,5340,5342],{"className":5341,"ariaHidden":610},[651],[574,5343,5345,5348],{"className":5344},[655],[574,5346],{"className":5347,"style":2242},[659],[574,5349,5351,5354],{"className":5350},[664],[574,5352,2151],{"className":5353},[664,665],[574,5355,5357],{"className":5356},[753],[574,5358,5360,5380],{"className":5359},[700,757],[574,5361,5363,5377],{"className":5362},[704],[574,5364,5366],{"className":5365,"style":1021},[708],[574,5367,5368,5371],{"style":767},[574,5369],{"className":5370,"style":771},[716],[574,5372,5374],{"className":5373},[775,776,777,778],[574,5375,595],{"className":5376,"style":666},[664,665,778],[574,5378,786],{"className":5379},[785],[574,5381,5383],{"className":5382},[704],[574,5384,5386],{"className":5385,"style":793},[708],[574,5387],{}," gleich ",[574,5390,5392,5416],{"className":5391},[577],[574,5393,5395],{"className":5394},[581],[583,5396,5397],{"xmlns":585},[587,5398,5399,5413],{},[590,5400,5401,5403,5405,5407,5409,5411],{},[597,5402,603],{"stretchy":602},[618,5404,3056],{},[597,5406,623],{"separator":610},[1606,5408,2675],{},[618,5410,620],{},[597,5412,642],{"stretchy":602},[644,5414,5415],{"encoding":646},"(2,\\ 1)",[574,5417,5419],{"className":5418,"ariaHidden":610},[651],[574,5420,5422,5425,5428,5431,5434,5437,5440,5443],{"className":5421},[655],[574,5423],{"className":5424,"style":961},[659],[574,5426,603],{"className":5427},[689],[574,5429,3056],{"className":5430},[664],[574,5432,623],{"className":5433},[799],[574,5435,2675],{"className":5436},[670],[574,5438],{"className":5439,"style":803},[670],[574,5441,620],{"className":5442},[664],[574,5444,642],{"className":5445},[893],". Spur (",[574,5448,5450,5463],{"className":5449},[577],[574,5451,5453],{"className":5452},[581],[583,5454,5455],{"xmlns":585},[587,5456,5457,5461],{},[590,5458,5459],{},[618,5460,3056],{},[644,5462,3056],{"encoding":646},[574,5464,5466],{"className":5465,"ariaHidden":610},[651],[574,5467,5469,5472],{"className":5468},[655],[574,5470],{"className":5471,"style":3823},[659],[574,5473,3056],{"className":5474},[664],") und Determinante (",[574,5477,5479,5492],{"className":5478},[577],[574,5480,5482],{"className":5481},[581],[583,5483,5484],{"xmlns":585},[587,5485,5486,5490],{},[590,5487,5488],{},[618,5489,620],{},[644,5491,620],{"encoding":646},[574,5493,5495],{"className":5494,"ariaHidden":610},[651],[574,5496,5498,5501],{"className":5497},[655],[574,5499],{"className":5500,"style":3823},[659],[574,5502,620],{"className":5503},[664],") stimmen mit denen von ",[574,5506,5508,5521],{"className":5507},[577],[574,5509,5511],{"className":5510},[581],[583,5512,5513],{"xmlns":585},[587,5514,5515,5519],{},[590,5516,5517],{},[593,5518,2151],{},[644,5520,2151],{"encoding":646},[574,5522,5524],{"className":5523,"ariaHidden":610},[651],[574,5525,5527,5530],{"className":5526},[655],[574,5528],{"className":5529,"style":660},[659],[574,5531,2151],{"className":5532},[664,665]," überein.",[560,5535,5537],{"id":5536},"typische-fehler","Typische Fehler",[1771,5539,5540,6012,6393],{},[1774,5541,5542,3024,5570,5638,5639,5818,5819,5945,5946,6011],{},[574,5543,5545,5558],{"className":5544},[577],[574,5546,5548],{"className":5547},[581],[583,5549,5550],{"xmlns":585},[587,5551,5552,5556],{},[590,5553,5554],{},[593,5555,1566],{},[644,5557,1566],{"encoding":646},[574,5559,5561],{"className":5560,"ariaHidden":610},[651],[574,5562,5564,5567],{"className":5563},[655],[574,5565],{"className":5566,"style":660},[659],[574,5568,1566],{"className":5569,"style":1581},[664,665],[574,5571,5573,5594],{"className":5572},[577],[574,5574,5576],{"className":5575},[581],[583,5577,5578],{"xmlns":585},[587,5579,5580,5592],{},[590,5581,5582],{},[1808,5583,5584,5586],{},[593,5585,1566],{},[590,5587,5588,5590],{},[597,5589,1816],{},[618,5591,620],{},[644,5593,2085],{"encoding":646},[574,5595,5597],{"className":5596,"ariaHidden":610},[651],[574,5598,5600,5603],{"className":5599},[655],[574,5601],{"className":5602,"style":1930},[659],[574,5604,5606,5609],{"className":5605},[664],[574,5607,1566],{"className":5608,"style":1581},[664,665],[574,5610,5612],{"className":5611},[753],[574,5613,5615],{"className":5614},[700],[574,5616,5618],{"className":5617},[704],[574,5619,5621],{"className":5620,"style":1930},[708],[574,5622,5623,5626],{"style":1951},[574,5624],{"className":5625,"style":771},[716],[574,5627,5629],{"className":5628},[775,776,777,778],[574,5630,5632,5635],{"className":5631},[664,778],[574,5633,1816],{"className":5634},[664,778],[574,5636,620],{"className":5637},[664,778]," vertauschen, also ",[574,5640,5642,5678],{"className":5641},[577],[574,5643,5645],{"className":5644},[581],[583,5646,5647],{"xmlns":585},[587,5648,5649,5675],{},[590,5650,5651,5653,5659,5665,5667,5669],{},[597,5652,909],{"stretchy":602},[608,5654,5655,5657],{"accent":610},[593,5656,914],{},[597,5658,616],{},[605,5660,5661,5663],{},[597,5662,921],{"stretchy":602},[593,5664,595],{},[597,5666,599],{},[593,5668,1566],{},[608,5670,5671,5673],{"accent":610},[593,5672,914],{},[597,5674,616],{},[644,5676,5677],{"encoding":646},"[\\vec v]_B = S\\vec v",[574,5679,5681,5774],{"className":5680,"ariaHidden":610},[651],[574,5682,5684,5687,5690,5725,5765,5768,5771],{"className":5683},[655],[574,5685],{"className":5686,"style":961},[659],[574,5688,909],{"className":5689},[689],[574,5691,5693],{"className":5692},[664,696],[574,5694,5696],{"className":5695},[700],[574,5697,5699],{"className":5698},[704],[574,5700,5702,5710],{"className":5701,"style":977},[708],[574,5703,5704,5707],{"style":712},[574,5705],{"className":5706,"style":717},[716],[574,5708,914],{"className":5709,"style":986},[664,665],[574,5711,5712,5715],{"style":712},[574,5713],{"className":5714,"style":717},[716],[574,5716,5718],{"className":5717,"style":995},[730],[574,5719,5721],{"className":5720,"style":736},[735],[738,5722,5723],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,5724],{"d":749},[574,5726,5728,5731],{"className":5727},[893],[574,5729,921],{"className":5730},[893],[574,5732,5734],{"className":5733},[753],[574,5735,5737,5757],{"className":5736},[700,757],[574,5738,5740,5754],{"className":5739},[704],[574,5741,5743],{"className":5742,"style":1021},[708],[574,5744,5745,5748],{"style":767},[574,5746],{"className":5747,"style":771},[716],[574,5749,5751],{"className":5750},[775,776,777,778],[574,5752,595],{"className":5753,"style":666},[664,665,778],[574,5755,786],{"className":5756},[785],[574,5758,5760],{"className":5759},[704],[574,5761,5763],{"className":5762,"style":793},[708],[574,5764],{},[574,5766],{"className":5767,"style":671},[670],[574,5769,599],{"className":5770},[675],[574,5772],{"className":5773,"style":671},[670],[574,5775,5777,5780,5783],{"className":5776},[655],[574,5778],{"className":5779,"style":977},[659],[574,5781,1566],{"className":5782,"style":1581},[664,665],[574,5784,5786],{"className":5785},[664,696],[574,5787,5789],{"className":5788},[700],[574,5790,5792],{"className":5791},[704],[574,5793,5795,5803],{"className":5794,"style":977},[708],[574,5796,5797,5800],{"style":712},[574,5798],{"className":5799,"style":717},[716],[574,5801,914],{"className":5802,"style":986},[664,665],[574,5804,5805,5808],{"style":712},[574,5806],{"className":5807,"style":717},[716],[574,5809,5811],{"className":5810,"style":995},[730],[574,5812,5814],{"className":5813,"style":736},[735],[738,5815,5816],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,5817],{"d":749}," rechnen. Probe: ",[574,5820,5822,5852],{"className":5821},[577],[574,5823,5825],{"className":5824},[581],[583,5826,5827],{"xmlns":585},[587,5828,5829,5849],{},[590,5830,5831,5833,5835,5837,5843],{},[593,5832,1566],{},[1606,5834,1608],{},[597,5836,909],{"stretchy":602},[608,5838,5839,5841],{"accent":610},[593,5840,914],{},[597,5842,616],{},[605,5844,5845,5847],{},[597,5846,921],{"stretchy":602},[593,5848,595],{},[644,5850,5851],{"encoding":646},"S\\,[\\vec v]_B",[574,5853,5855],{"className":5854,"ariaHidden":610},[651],[574,5856,5858,5861,5864,5867,5870,5905],{"className":5857},[655],[574,5859],{"className":5860,"style":961},[659],[574,5862,1566],{"className":5863,"style":1581},[664,665],[574,5865],{"className":5866,"style":803},[670],[574,5868,909],{"className":5869},[689],[574,5871,5873],{"className":5872},[664,696],[574,5874,5876],{"className":5875},[700],[574,5877,5879],{"className":5878},[704],[574,5880,5882,5890],{"className":5881,"style":977},[708],[574,5883,5884,5887],{"style":712},[574,5885],{"className":5886,"style":717},[716],[574,5888,914],{"className":5889,"style":986},[664,665],[574,5891,5892,5895],{"style":712},[574,5893],{"className":5894,"style":717},[716],[574,5896,5898],{"className":5897,"style":995},[730],[574,5899,5901],{"className":5900,"style":736},[735],[738,5902,5903],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,5904],{"d":749},[574,5906,5908,5911],{"className":5907},[893],[574,5909,921],{"className":5910},[893],[574,5912,5914],{"className":5913},[753],[574,5915,5917,5937],{"className":5916},[700,757],[574,5918,5920,5934],{"className":5919},[704],[574,5921,5923],{"className":5922,"style":1021},[708],[574,5924,5925,5928],{"style":767},[574,5926],{"className":5927,"style":771},[716],[574,5929,5931],{"className":5930},[775,776,777,778],[574,5932,595],{"className":5933,"style":666},[664,665,778],[574,5935,786],{"className":5936},[785],[574,5938,5940],{"className":5939},[704],[574,5941,5943],{"className":5942,"style":793},[708],[574,5944],{}," muss wieder ",[574,5947,5949,5967],{"className":5948},[577],[574,5950,5952],{"className":5951},[581],[583,5953,5954],{"xmlns":585},[587,5955,5956,5964],{},[590,5957,5958],{},[608,5959,5960,5962],{"accent":610},[593,5961,914],{},[597,5963,616],{},[644,5965,5966],{"encoding":646},"\\vec v",[574,5968,5970],{"className":5969,"ariaHidden":610},[651],[574,5971,5973,5976],{"className":5972},[655],[574,5974],{"className":5975,"style":977},[659],[574,5977,5979],{"className":5978},[664,696],[574,5980,5982],{"className":5981},[700],[574,5983,5985],{"className":5984},[704],[574,5986,5988,5996],{"className":5987,"style":977},[708],[574,5989,5990,5993],{"style":712},[574,5991],{"className":5992,"style":717},[716],[574,5994,914],{"className":5995,"style":986},[664,665],[574,5997,5998,6001],{"style":712},[574,5999],{"className":6000,"style":717},[716],[574,6002,6004],{"className":6003,"style":995},[730],[574,6005,6007],{"className":6006,"style":736},[735],[738,6008,6009],{"xmlns":740,"width":741,"height":742,"style":743,"viewBox":744,"preserveAspectRatio":745},[747,6010],{"d":749}," ergeben.",[1774,6013,6014,6156,6157,6185,6186,6265,6266,6294,6295,6323,6324,6392],{},[574,6015,6017,6051],{"className":6016},[577],[574,6018,6020],{"className":6019},[581],[583,6021,6022],{"xmlns":585},[587,6023,6024,6048],{},[590,6025,6026,6032,6034,6036,6038],{},[605,6027,6028,6030],{},[593,6029,2151],{},[593,6031,595],{},[597,6033,599],{},[593,6035,1566],{},[593,6037,2151],{},[1808,6039,6040,6042],{},[593,6041,1566],{},[590,6043,6044,6046],{},[597,6045,1816],{},[618,6047,620],{},[644,6049,6050],{"encoding":646},"A_B = S A S^{-1}",[574,6052,6054,6109],{"className":6053,"ariaHidden":610},[651],[574,6055,6057,6060,6100,6103,6106],{"className":6056},[655],[574,6058],{"className":6059,"style":2242},[659],[574,6061,6063,6066],{"className":6062},[664],[574,6064,2151],{"className":6065},[664,665],[574,6067,6069],{"className":6068},[753],[574,6070,6072,6092],{"className":6071},[700,757],[574,6073,6075,6089],{"className":6074},[704],[574,6076,6078],{"className":6077,"style":1021},[708],[574,6079,6080,6083],{"style":767},[574,6081],{"className":6082,"style":771},[716],[574,6084,6086],{"className":6085},[775,776,777,778],[574,6087,595],{"className":6088,"style":666},[664,665,778],[574,6090,786],{"className":6091},[785],[574,6093,6095],{"className":6094},[704],[574,6096,6098],{"className":6097,"style":793},[708],[574,6099],{},[574,6101],{"className":6102,"style":671},[670],[574,6104,599],{"className":6105},[675],[574,6107],{"className":6108,"style":671},[670],[574,6110,6112,6115,6118,6121],{"className":6111},[655],[574,6113],{"className":6114,"style":1930},[659],[574,6116,1566],{"className":6117,"style":1581},[664,665],[574,6119,2151],{"className":6120},[664,665],[574,6122,6124,6127],{"className":6123},[664],[574,6125,1566],{"className":6126,"style":1581},[664,665],[574,6128,6130],{"className":6129},[753],[574,6131,6133],{"className":6132},[700],[574,6134,6136],{"className":6135},[704],[574,6137,6139],{"className":6138,"style":1930},[708],[574,6140,6141,6144],{"style":1951},[574,6142],{"className":6143,"style":771},[716],[574,6145,6147],{"className":6146},[775,776,777,778],[574,6148,6150,6153],{"className":6149},[664,778],[574,6151,1816],{"className":6152},[664,778],[574,6154,620],{"className":6155},[664,778]," schreiben. Mit den Basisvektoren als Spalten von ",[574,6158,6160,6173],{"className":6159},[577],[574,6161,6163],{"className":6162},[581],[583,6164,6165],{"xmlns":585},[587,6166,6167,6171],{},[590,6168,6169],{},[593,6170,1566],{},[644,6172,1566],{"encoding":646},[574,6174,6176],{"className":6175,"ariaHidden":610},[651],[574,6177,6179,6182],{"className":6178},[655],[574,6180],{"className":6181,"style":660},[659],[574,6183,1566],{"className":6184,"style":1581},[664,665]," ist das falsch. Die Form ",[574,6187,6189,6215],{"className":6188},[577],[574,6190,6192],{"className":6191},[581],[583,6193,6194],{"xmlns":585},[587,6195,6196,6212],{},[590,6197,6198,6200,6202],{},[593,6199,1566],{},[593,6201,2151],{},[1808,6203,6204,6206],{},[593,6205,1566],{},[590,6207,6208,6210],{},[597,6209,1816],{},[618,6211,620],{},[644,6213,6214],{"encoding":646},"S A S^{-1}",[574,6216,6218],{"className":6217,"ariaHidden":610},[651],[574,6219,6221,6224,6227,6230],{"className":6220},[655],[574,6222],{"className":6223,"style":1930},[659],[574,6225,1566],{"className":6226,"style":1581},[664,665],[574,6228,2151],{"className":6229},[664,665],[574,6231,6233,6236],{"className":6232},[664],[574,6234,1566],{"className":6235,"style":1581},[664,665],[574,6237,6239],{"className":6238},[753],[574,6240,6242],{"className":6241},[700],[574,6243,6245],{"className":6244},[704],[574,6246,6248],{"className":6247,"style":1930},[708],[574,6249,6250,6253],{"style":1951},[574,6251],{"className":6252,"style":771},[716],[574,6254,6256],{"className":6255},[775,776,777,778],[574,6257,6259,6262],{"className":6258},[664,778],[574,6260,1816],{"className":6261},[664,778],[574,6263,620],{"className":6264},[664,778]," passt nur, wenn ",[574,6267,6269,6282],{"className":6268},[577],[574,6270,6272],{"className":6271},[581],[583,6273,6274],{"xmlns":585},[587,6275,6276,6280],{},[590,6277,6278],{},[593,6279,1566],{},[644,6281,1566],{"encoding":646},[574,6283,6285],{"className":6284,"ariaHidden":610},[651],[574,6286,6288,6291],{"className":6287},[655],[574,6289],{"className":6290,"style":660},[659],[574,6292,1566],{"className":6293,"style":1581},[664,665]," selbst die Umrechnung von Standard- nach ",[574,6296,6298,6311],{"className":6297},[577],[574,6299,6301],{"className":6300},[581],[583,6302,6303],{"xmlns":585},[587,6304,6305,6309],{},[590,6306,6307],{},[593,6308,595],{},[644,6310,595],{"encoding":646},[574,6312,6314],{"className":6313,"ariaHidden":610},[651],[574,6315,6317,6320],{"className":6316},[655],[574,6318],{"className":6319,"style":660},[659],[574,6321,595],{"className":6322,"style":666},[664,665],"-Koordinaten beschreibt, also die Rolle von ",[574,6325,6327,6348],{"className":6326},[577],[574,6328,6330],{"className":6329},[581],[583,6331,6332],{"xmlns":585},[587,6333,6334,6346],{},[590,6335,6336],{},[1808,6337,6338,6340],{},[593,6339,1566],{},[590,6341,6342,6344],{},[597,6343,1816],{},[618,6345,620],{},[644,6347,2085],{"encoding":646},[574,6349,6351],{"className":6350,"ariaHidden":610},[651],[574,6352,6354,6357],{"className":6353},[655],[574,6355],{"className":6356,"style":1930},[659],[574,6358,6360,6363],{"className":6359},[664],[574,6361,1566],{"className":6362,"style":1581},[664,665],[574,6364,6366],{"className":6365},[753],[574,6367,6369],{"className":6368},[700],[574,6370,6372],{"className":6371},[704],[574,6373,6375],{"className":6374,"style":1930},[708],[574,6376,6377,6380],{"style":1951},[574,6378],{"className":6379,"style":771},[716],[574,6381,6383],{"className":6382},[775,776,777,778],[574,6384,6386,6389],{"className":6385},[664,778],[574,6387,1816],{"className":6388},[664,778],[574,6390,620],{"className":6391},[664,778]," hat.",[1774,6394,6395,6396,6424],{},"Die Basisvektoren als Zeilen statt als Spalten in ",[574,6397,6399,6412],{"className":6398},[577],[574,6400,6402],{"className":6401},[581],[583,6403,6404],{"xmlns":585},[587,6405,6406,6410],{},[590,6407,6408],{},[593,6409,1566],{},[644,6411,1566],{"encoding":646},[574,6413,6415],{"className":6414,"ariaHidden":610},[651],[574,6416,6418,6421],{"className":6417},[655],[574,6419],{"className":6420,"style":660},[659],[574,6422,1566],{"className":6423,"style":1581},[664,665]," eintragen.",{"title":6426,"searchDepth":6427,"depth":6427,"links":6428},"",2,[6429,6430,6431],{"id":562,"depth":6427,"text":563},{"id":2643,"depth":6427,"text":2644},{"id":5536,"depth":6427,"text":5537},[6433,6435,6437,6439,6441,6443,6445,6448,6450,6452,6454,6456,6458,6460,6463],{"lhs":6434,"rhs":565},"multiply([[a + 3, b], [c, d + 3]], multiply(inv([[a + 3, b], [c, d + 3]]), [p, q]))[1]",{"lhs":6436,"rhs":3056},"multiply(inv([[1, 1], [1, -1]]), [3, 1])[1]",{"lhs":6438,"rhs":620},"multiply(inv([[1, 1], [1, -1]]), [3, 1])[2]",{"lhs":6440,"rhs":3385},"2*1 + 1*1",{"lhs":6442,"rhs":620},"2*1 + 1*(-1)",{"lhs":6444,"rhs":3056},"multiply(inv([[1, 1], [1, -1]]), multiply([[1, 2], [0, 1]], [[1, 1], [1, -1]]))[1, 1]",{"lhs":6446,"rhs":6447},"multiply(inv([[1, 1], [1, -1]]), multiply([[1, 2], [0, 1]], [[1, 1], [1, -1]]))[1, 2]","-1",{"lhs":6449,"rhs":620},"multiply(inv([[1, 1], [1, -1]]), multiply([[1, 2], [0, 1]], [[1, 1], [1, -1]]))[2, 1]",{"lhs":6451,"rhs":2835},"multiply(inv([[1, 1], [1, -1]]), multiply([[1, 2], [0, 1]], [[1, 1], [1, -1]]))[2, 2]",{"lhs":6453,"rhs":3385},"multiply([[1, 2], [0, 1]], [[1, 1], [1, -1]])[1, 1]",{"lhs":6455,"rhs":6447},"multiply([[1, 2], [0, 1]], [[1, 1], [1, -1]])[1, 2]",{"lhs":6440,"rhs":6457},"1*1 + 2*1",{"lhs":6442,"rhs":6459},"0*1 + 1*1",{"lhs":6461,"rhs":6462},"2 + 0","1 + 1",{"lhs":6464,"rhs":6465},"2*0 - (-1)*1","1*1 - 2*0","\\vec b_1, \\ldots, \\vec b_n \\text{ Basis des } \\mathbb{R}^n,\\ A \\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>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec b_1, \\ldots, \\vec b_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:1.1719em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">Basis des\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\mathbb{R}^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:0.8833em;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:0.6644em;\">\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 mathnormal mtight\">n\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>A\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>×\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\in \\mathbb{R}^{n \\times n}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7224em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7713em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","change-of-basis","[\\vec v]_B = S^{-1} \\vec v, \\qquad A_B = S^{-1} A\\, S, \\qquad S = (\\vec b_1 \\mid \\cdots \\mid \\vec b_n)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmsub>\u003Cmo stretchy=\"false\">]\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>S\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmover accent=\"true\">\u003Cmi>v\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsup>\u003Cmi>S\u003C\u002Fmi>\u003Cmrow>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>S\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>S\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>∣\u003C\u002Fmo>\u003Cmo>⋯\u003C\u002Fmo>\u003Cmo>∣\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">[\\vec v]_B = S^{-1} \\vec v, \\qquad A_B = S^{-1} A\\, S, \\qquad S = (\\vec b_1 \\mid \\cdots \\mid \\vec b_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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan 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