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",[570,2170,2172,2194],{"className":2171},[573],[570,2173,2175],{"className":2174},[577],[579,2176,2177],{"xmlns":581},[583,2178,2179,2191],{},[586,2180,2181,2183,2185,2187,2189],{},[589,2182,1611],{},[637,2184,1614],{},[589,2186,591],{},[637,2188,1029],{"mathvariant":1028},[1033,2190,1035],{},[593,2192,2193],{"encoding":595},"\\det A \\neq 0",[570,2195,2197,2254],{"className":2196,"ariaHidden":600},[599],[570,2198,2200,2203,2206,2209,2212,2215,2251],{"className":2199},[604],[570,2201],{"className":2202,"style":1110},[608],[570,2204,1611],{"className":2205},[1657],[570,2207],{"className":2208,"style":1661},[760],[570,2210,591],{"className":2211},[613,614],[570,2213],{"className":2214,"style":761},[760],[570,2216,2218,2245,2248],{"className":2217},[765],[570,2219,2221],{"className":2220},[765],[570,2222,2224],{"className":2223},[613,1098],[570,2225,2227],{"className":2226},[1102],[570,2228,2230,2233,2242],{"className":2229},[1106],[570,2231],{"className":2232,"style":1110},[608],[570,2234,2236],{"className":2235},[1114],[570,2237,2239],{"className":2238},[613],[570,2240,1121],{"className":2241},[765],[570,2243],{"className":2244},[1125],[570,2246],{"className":2247},[760,1129],[570,2249,655],{"className":2250},[765],[570,2252],{"className":2253,"style":761},[760],[570,2255,2257,2260],{"className":2256},[604],[570,2258],{"className":2259,"style":1237},[608],[570,2261,1035],{"className":2262},[613]," und keins der beiden Muster liegt vor, ist ",[570,2265,2267,2280],{"className":2266},[573],[570,2268,2270],{"className":2269},[577],[579,2271,2272],{"xmlns":581},[583,2273,2274,2278],{},[586,2275,2276],{},[589,2277,591],{},[593,2279,591],{"encoding":595},[570,2281,2283],{"className":2282,"ariaHidden":600},[599],[570,2284,2286,2289],{"className":2285},[604],[570,2287],{"className":2288,"style":609},[608],[570,2290,591],{"className":2291},[613,614],[617,2293,552],{},".",[566,2296,2297,2298,2301,2302,2305],{},"Für ",[617,2299,2300],{},"Semidefinitheit"," reichen die führenden Hauptminoren nicht: Man muss ",[617,2303,2304],{},"alle"," Hauptminoren prüfen (alle Teilmatrizen mit gleicher Zeilen- und Spaltenauswahl) oder die Eigenwerte.",[566,2307,2308],{},"Anwendung: Bei Funktionen mehrerer Variablen entscheidet die Definitheit der Hesse-Matrix, ob ein kritischer Punkt ein Minimum (positiv definit), ein Maximum (negativ definit) oder ein Sattelpunkt (indefinit) ist.",[561,2310,2312],{"id":2311},"beispiele","Beispiele",[566,2314,2315,2747,2748,2776,2777,3067,3068,3131,3132,3160],{},[570,2316,2318,2426],{"className":2317},[573],[570,2319,2321],{"className":2320},[577],[579,2322,2323],{"xmlns":581},[583,2324,2325,2423],{},[586,2326,2327,2329,2331],{},[589,2328,591],{},[637,2330,655],{},[586,2332,2333,2335,2421],{},[637,2334,640],{"fence":600},[2336,2337,2341,2369,2397],"mtable",{"rowspacing":2338,"columnalign":2339,"columnspacing":2340},"0.16em","center center center","1em",[2342,2343,2344,2353,2363],"mtr",{},[2345,2346,2347],"mtd",{},[2348,2349,2350],"mstyle",{"scriptlevel":1035,"displaystyle":639},[1033,2351,2352],{},"2",[2345,2354,2355],{},[2348,2356,2357],{"scriptlevel":1035,"displaystyle":639},[586,2358,2359,2361],{},[637,2360,1991],{},[1033,2362,1622],{},[2345,2364,2365],{},[2348,2366,2367],{"scriptlevel":1035,"displaystyle":639},[1033,2368,1035],{},[2342,2370,2371,2381,2387],{},[2345,2372,2373],{},[2348,2374,2375],{"scriptlevel":1035,"displaystyle":639},[586,2376,2377,2379],{},[637,2378,1991],{},[1033,2380,1622],{},[2345,2382,2383],{},[2348,2384,2385],{"scriptlevel":1035,"displaystyle":639},[1033,2386,2352],{},[2345,2388,2389],{},[2348,2390,2391],{"scriptlevel":1035,"displaystyle":639},[586,2392,2393,2395],{},[637,2394,1991],{},[1033,2396,1622],{},[2342,2398,2399,2405,2415],{},[2345,2400,2401],{},[2348,2402,2403],{"scriptlevel":1035,"displaystyle":639},[1033,2404,1035],{},[2345,2406,2407],{},[2348,2408,2409],{"scriptlevel":1035,"displaystyle":639},[586,2410,2411,2413],{},[637,2412,1991],{},[1033,2414,1622],{},[2345,2416,2417],{},[2348,2418,2419],{"scriptlevel":1035,"displaystyle":639},[1033,2420,2352],{},[637,2422,652],{"fence":600},[593,2424,2425],{"encoding":595},"A = \\begin{pmatrix} 2 & -1 & 0 \\\\ -1 & 2 & -1 \\\\ 0 & -1 & 2 \\end{pmatrix}",[570,2427,2429,2447],{"className":2428,"ariaHidden":600},[599],[570,2430,2432,2435,2438,2441,2444],{"className":2431},[604],[570,2433],{"className":2434,"style":609},[608],[570,2436,591],{"className":2437},[613,614],[570,2439],{"className":2440,"style":761},[760],[570,2442,655],{"className":2443},[765],[570,2445],{"className":2446,"style":761},[760],[570,2448,2450,2454],{"className":2449},[604],[570,2451],{"className":2452,"style":2453},[608],"height:3.6em;vertical-align:-1.55em;",[570,2455,2457,2505,2709],{"className":2456},[1718],[570,2458,2460],{"className":2459},[696],[570,2461,2465],{"className":2462},[2463,2464],"delimsizing","mult",[570,2466,2468,2496],{"className":2467},[704,1674],[570,2469,2471,2493],{"className":2470},[708],[570,2472,2475],{"className":2473,"style":2474},[712],"height:2.05em;",[570,2476,2478,2482],{"style":2477},"top:-4.05em;",[570,2479],{"className":2480,"style":2481},[720],"height:5.6em;",[570,2483,2485],{"style":2484},"width:0.875em;height:3.6em;",[741,2486,2490],{"xmlns":743,"width":2487,"height":2488,"viewBox":2489},"0.875em","3.6em","0 0 875 3600",[750,2491],{"d":2492},"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",[570,2494,1698],{"className":2495},[1697],[570,2497,2499],{"className":2498},[708],[570,2500,2503],{"className":2501,"style":2502},[712],"height:1.55em;",[570,2504],{},[570,2506,2508],{"className":2507},[613],[570,2509,2511,2574,2579,2582,2644,2647,2650],{"className":2510},[2336],[570,2512,2515],{"className":2513},[2514],"col-align-c",[570,2516,2518,2566],{"className":2517},[704,1674],[570,2519,2521,2563],{"className":2520},[708],[570,2522,2524,2536,2551],{"className":2523,"style":2474},[712],[570,2525,2527,2530],{"style":2526},"top:-4.21em;",[570,2528],{"className":2529,"style":721},[720],[570,2531,2533],{"className":2532},[613],[570,2534,2352],{"className":2535},[613],[570,2537,2539,2542],{"style":2538},"top:-3.01em;",[570,2540],{"className":2541,"style":721},[720],[570,2543,2545,2548],{"className":2544},[613],[570,2546,1991],{"className":2547},[613],[570,2549,1622],{"className":2550},[613],[570,2552,2554,2557],{"style":2553},"top:-1.81em;",[570,2555],{"className":2556,"style":721},[720],[570,2558,2560],{"className":2559},[613],[570,2561,1035],{"className":2562},[613],[570,2564,1698],{"className":2565},[1697],[570,2567,2569],{"className":2568},[708],[570,2570,2572],{"className":2571,"style":2502},[712],[570,2573],{},[570,2575],{"className":2576,"style":2578},[2577],"arraycolsep","width:0.5em;",[570,2580],{"className":2581,"style":2578},[2577],[570,2583,2585],{"className":2584},[2514],[570,2586,2588,2636],{"className":2587},[704,1674],[570,2589,2591,2633],{"className":2590},[708],[570,2592,2594,2608,2619],{"className":2593,"style":2474},[712],[570,2595,2596,2599],{"style":2526},[570,2597],{"className":2598,"style":721},[720],[570,2600,2602,2605],{"className":2601},[613],[570,2603,1991],{"className":2604},[613],[570,2606,1622],{"className":2607},[613],[570,2609,2610,2613],{"style":2538},[570,2611],{"className":2612,"style":721},[720],[570,2614,2616],{"className":2615},[613],[570,2617,2352],{"className":2618},[613],[570,2620,2621,2624],{"style":2553},[570,2622],{"className":2623,"style":721},[720],[570,2625,2627,2630],{"className":2626},[613],[570,2628,1991],{"className":2629},[613],[570,2631,1622],{"className":2632},[613],[570,2634,1698],{"className":2635},[1697],[570,2637,2639],{"className":2638},[708],[570,2640,2642],{"className":2641,"style":2502},[712],[570,2643],{},[570,2645],{"className":2646,"style":2578},[2577],[570,2648],{"className":2649,"style":2578},[2577],[570,2651,2653],{"className":2652},[2514],[570,2654,2656,2701],{"className":2655},[704,1674],[570,2657,2659,2698],{"className":2658},[708],[570,2660,2662,2673,2687],{"className":2661,"style":2474},[712],[570,2663,2664,2667],{"style":2526},[570,2665],{"className":2666,"style":721},[720],[570,2668,2670],{"className":2669},[613],[570,2671,1035],{"className":2672},[613],[570,2674,2675,2678],{"style":2538},[570,2676],{"className":2677,"style":721},[720],[570,2679,2681,2684],{"className":2680},[613],[570,2682,1991],{"className":2683},[613],[570,2685,1622],{"className":2686},[613],[570,2688,2689,2692],{"style":2553},[570,2690],{"className":2691,"style":721},[720],[570,2693,2695],{"className":2694},[613],[570,2696,2352],{"className":2697},[613],[570,2699,1698],{"className":2700},[1697],[570,2702,2704],{"className":2703},[708],[570,2705,2707],{"className":2706,"style":2502},[712],[570,2708],{},[570,2710,2712],{"className":2711},[756],[570,2713,2715],{"className":2714},[2463,2464],[570,2716,2718,2739],{"className":2717},[704,1674],[570,2719,2721,2736],{"className":2720},[708],[570,2722,2724],{"className":2723,"style":2474},[712],[570,2725,2726,2729],{"style":2477},[570,2727],{"className":2728,"style":2481},[720],[570,2730,2731],{"style":2484},[741,2732,2733],{"xmlns":743,"width":2487,"height":2488,"viewBox":2489},[750,2734],{"d":2735},"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",[570,2737,1698],{"className":2738},[1697],[570,2740,2742],{"className":2741},[708],[570,2743,2745],{"className":2744,"style":2502},[712],[570,2746],{}," hat die führenden Hauptminoren ",[570,2749,2751,2764],{"className":2750},[573],[570,2752,2754],{"className":2753},[577],[579,2755,2756],{"xmlns":581},[583,2757,2758,2762],{},[586,2759,2760],{},[1033,2761,2352],{},[593,2763,2352],{"encoding":595},[570,2765,2767],{"className":2766,"ariaHidden":600},[599],[570,2768,2770,2773],{"className":2769},[604],[570,2771],{"className":2772,"style":1237},[608],[570,2774,2352],{"className":2775},[613],", ",[570,2778,2780,2843],{"className":2779},[573],[570,2781,2783],{"className":2782},[577],[579,2784,2785],{"xmlns":581},[583,2786,2787,2840],{},[586,2788,2789,2835,2837],{},[586,2790,2791,2794,2833],{},[637,2792,2793],{"fence":600},"∣",[2336,2795,2797,2815],{"rowspacing":2338,"columnalign":2796,"columnspacing":2340},"center center",[2342,2798,2799,2805],{},[2345,2800,2801],{},[2348,2802,2803],{"scriptlevel":1035,"displaystyle":639},[1033,2804,2352],{},[2345,2806,2807],{},[2348,2808,2809],{"scriptlevel":1035,"displaystyle":639},[586,2810,2811,2813],{},[637,2812,1991],{},[1033,2814,1622],{},[2342,2816,2817,2827],{},[2345,2818,2819],{},[2348,2820,2821],{"scriptlevel":1035,"displaystyle":639},[586,2822,2823,2825],{},[637,2824,1991],{},[1033,2826,1622],{},[2345,2828,2829],{},[2348,2830,2831],{"scriptlevel":1035,"displaystyle":639},[1033,2832,2352],{},[637,2834,2793],{"fence":600},[637,2836,655],{},[1033,2838,2839],{},"3",[593,2841,2842],{"encoding":595},"\\begin{vmatrix} 2 & -1 \\\\ -1 & 2 \\end{vmatrix} = 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Alle sind positiv, ",[570,3133,3135,3148],{"className":3134},[573],[570,3136,3138],{"className":3137},[577],[579,3139,3140],{"xmlns":581},[583,3141,3142,3146],{},[586,3143,3144],{},[589,3145,591],{},[593,3147,591],{"encoding":595},[570,3149,3151],{"className":3150,"ariaHidden":600},[599],[570,3152,3154,3157],{"className":3153},[604],[570,3155],{"className":3156,"style":609},[608],[570,3158,591],{"className":3159},[613,614]," ist positiv definit. Man sieht es auch an der quadratischen 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hat die Minoren ",[570,4933,4935,4955],{"className":4934},[573],[570,4936,4938],{"className":4937},[577],[579,4939,4940],{"xmlns":581},[583,4941,4942,4952],{},[586,4943,4944,4946,4948,4950],{},[637,4945,1991],{},[1033,4947,2352],{},[637,4949,1405],{},[1033,4951,1035],{},[593,4953,4954],{"encoding":595},"-2 \u003C 0",[570,4956,4958,4979],{"className":4957,"ariaHidden":600},[599],[570,4959,4961,4964,4967,4970,4973,4976],{"className":4960},[604],[570,4962],{"className":4963,"style":4304},[608],[570,4965,1991],{"className":4966},[613],[570,4968,2352],{"className":4969},[613],[570,4971],{"className":4972,"style":761},[760],[570,4974,1405],{"className":4975},[765],[570,4977],{"className":4978,"style":761},[760],[570,4980,4982,4985],{"className":4981},[604],[570,4983],{"className":4984,"style":1237},[608],[570,4986,1035],{"className":4987},[613],[570,4989,4991,5009],{"className":4990},[573],[570,4992,4994],{"className":4993},[577],[579,4995,4996],{"xmlns":581},[583,4997,4998,5006],{},[586,4999,5000,5002,5004],{},[1033,5001,2839],{},[637,5003,1209],{},[1033,5005,1035],{},[593,5007,5008],{"encoding":595},"3 > 0",[570,5010,5012,5030],{"className":5011,"ariaHidden":600},[599],[570,5013,5015,5018,5021,5024,5027],{"className":5014},[604],[570,5016],{"className":5017,"style":4217},[608],[570,5019,2839],{"className":5020},[613],[570,5022],{"className":5023,"style":761},[760],[570,5025,1209],{"className":5026},[765],[570,5028],{"className":5029,"style":761},[760],[570,5031,5033,5036],{"className":5032},[604],[570,5034],{"className":5035,"style":1237},[608],[570,5037,1035],{"className":5038},[613],", das Vorzeichen wechselt passend: negativ definit.",[561,5041,5043],{"id":5042},"typische-fehler","Typische Fehler",[1777,5045,5046,5416,5531,5711],{},[1780,5047,5048,5049,5091,5092,2747,5274,3067,5302,5330,5331,5415],{},"Aus führenden Hauptminoren ",[570,5050,5052,5067],{"className":5051},[573],[570,5053,5055],{"className":5054},[577],[579,5056,5057],{"xmlns":581},[583,5058,5059,5065],{},[586,5060,5061,5063],{},[637,5062,1308],{},[1033,5064,1035],{},[593,5066,1313],{"encoding":595},[570,5068,5070,5082],{"className":5069,"ariaHidden":600},[599],[570,5071,5073,5076,5079],{"className":5072},[604],[570,5074],{"className":5075,"style":1323},[608],[570,5077,1308],{"className":5078},[765],[570,5080],{"className":5081,"style":761},[760],[570,5083,5085,5088],{"className":5084},[604],[570,5086],{"className":5087,"style":1237},[608],[570,5089,1035],{"className":5090},[613]," auf positive Semidefinitheit schließen. ",[570,5093,5095,5145],{"className":5094},[573],[570,5096,5098],{"className":5097},[577],[579,5099,5100],{"xmlns":581},[583,5101,5102,5142],{},[586,5103,5104,5106,5140],{},[637,5105,640],{"fence":600},[2336,5107,5108,5122],{"rowspacing":2338,"columnalign":2796,"columnspacing":2340},[2342,5109,5110,5116],{},[2345,5111,5112],{},[2348,5113,5114],{"scriptlevel":1035,"displaystyle":639},[1033,5115,1035],{},[2345,5117,5118],{},[2348,5119,5120],{"scriptlevel":1035,"displaystyle":639},[1033,5121,1035],{},[2342,5123,5124,5130],{},[2345,5125,5126],{},[2348,5127,5128],{"scriptlevel":1035,"displaystyle":639},[1033,5129,1035],{},[2345,5131,5132],{},[2348,5133,5134],{"scriptlevel":1035,"displaystyle":639},[586,5135,5136,5138],{},[637,5137,1991],{},[1033,5139,1622],{},[637,5141,652],{"fence":600},[593,5143,5144],{"encoding":595},"\\begin{pmatrix} 0 & 0 \\\\ 0 & -1 \\end{pmatrix}",[570,5146,5148],{"className":5147,"ariaHidden":600},[599],[570,5149,5151,5154],{"className":5150},[604],[570,5152],{"className":5153,"style":2852},[608],[570,5155,5157,5163,5268],{"className":5156},[1718],[570,5158,5160],{"className":5159,"style":4001},[696,4000],[570,5161,640],{"className":5162},[2463,839],[570,5164,5166],{"className":5165},[613],[570,5167,5169,5214,5217,5220],{"className":5168},[2336],[570,5170,5172],{"className":5171},[2514],[570,5173,5175,5206],{"className":5174},[704,1674],[570,5176,5178,5203],{"className":5177},[708],[570,5179,5181,5192],{"className":5180,"style":2871},[712],[570,5182,5183,5186],{"style":2922},[570,5184],{"className":5185,"style":721},[720],[570,5187,5189],{"className":5188},[613],[570,5190,1035],{"className":5191},[613],[570,5193,5194,5197],{"style":2934},[570,5195],{"className":5196,"style":721},[720],[570,5198,5200],{"className":5199},[613],[570,5201,1035],{"className":5202},[613],[570,5204,1698],{"className":5205},[1697],[570,5207,5209],{"className":5208},[708],[570,5210,5212],{"className":5211,"style":2899},[712],[570,5213],{},[570,5215],{"className":5216,"style":2578},[2577],[570,5218],{"className":5219,"style":2578},[2577],[570,5221,5223],{"className":5222},[2514],[570,5224,5226,5260],{"className":5225},[704,1674],[570,5227,5229,5257],{"className":5228},[708],[570,5230,5232,5243],{"className":5231,"style":2871},[712],[570,5233,5234,5237],{"style":2922},[570,5235],{"className":5236,"style":721},[720],[570,5238,5240],{"className":5239},[613],[570,5241,1035],{"className":5242},[613],[570,5244,5245,5248],{"style":2934},[570,5246],{"className":5247,"style":721},[720],[570,5249,5251,5254],{"className":5250},[613],[570,5252,1991],{"className":5253},[613],[570,5255,1622],{"className":5256},[613],[570,5258,1698],{"className":5259},[1697],[570,5261,5263],{"className":5262},[708],[570,5264,5266],{"className":5265,"style":2899},[712],[570,5267],{},[570,5269,5271],{"className":5270,"style":4001},[756,4000],[570,5272,652],{"className":5273},[2463,839],[570,5275,5277,5290],{"className":5276},[573],[570,5278,5280],{"className":5279},[577],[579,5281,5282],{"xmlns":581},[583,5283,5284,5288],{},[586,5285,5286],{},[1033,5287,1035],{},[593,5289,1035],{"encoding":595},[570,5291,5293],{"className":5292,"ariaHidden":600},[599],[570,5294,5296,5299],{"className":5295},[604],[570,5297],{"className":5298,"style":1237},[608],[570,5300,1035],{"className":5301},[613],[570,5303,5305,5318],{"className":5304},[573],[570,5306,5308],{"className":5307},[577],[579,5309,5310],{"xmlns":581},[583,5311,5312,5316],{},[586,5313,5314],{},[1033,5315,1035],{},[593,5317,1035],{"encoding":595},[570,5319,5321],{"className":5320,"ariaHidden":600},[599],[570,5322,5324,5327],{"className":5323},[604],[570,5325],{"className":5326,"style":1237},[608],[570,5328,1035],{"className":5329},[613],", ist aber wegen ",[570,5332,5334,5364],{"className":5333},[573],[570,5335,5337],{"className":5336},[577],[579,5338,5339],{"xmlns":581},[583,5340,5341,5361],{},[586,5342,5343,5345,5347,5349,5351,5353,5355,5357,5359],{},[589,5344,635],{},[637,5346,640],{"stretchy":639},[1033,5348,1035],{},[637,5350,1625],{"separator":600},[1033,5352,1622],{},[637,5354,652],{"stretchy":639},[637,5356,655],{},[637,5358,1991],{},[1033,5360,1622],{},[593,5362,5363],{"encoding":595},"q(0, 1) = -1",[570,5365,5367,5403],{"className":5366,"ariaHidden":600},[599],[570,5368,5370,5373,5376,5379,5382,5385,5388,5391,5394,5397,5400],{"className":5369},[604],[570,5371],{"className":5372,"style":688},[608],[570,5374,635],{"className":5375,"style":692},[613,614],[570,5377,640],{"className":5378},[696],[570,5380,1035],{"className":5381},[613],[570,5383,1625],{"className":5384},[1711],[570,5386],{"className":5387,"style":1661},[760],[570,5389,1622],{"className":5390},[613],[570,5392,652],{"className":5393},[756],[570,5395],{"className":5396,"style":761},[760],[570,5398,655],{"className":5399},[765],[570,5401],{"className":5402,"style":761},[760],[570,5404,5406,5409,5412],{"className":5405},[604],[570,5407],{"className":5408,"style":4304},[608],[570,5410,1991],{"className":5411},[613],[570,5413,1622],{"className":5414},[613]," negativ semidefinit und nicht positiv semidefinit.",[1780,5417,5418,5419,5461,5462],{},"Für negative Definitheit „alle Minoren ",[570,5420,5422,5437],{"className":5421},[573],[570,5423,5425],{"className":5424},[577],[579,5426,5427],{"xmlns":581},[583,5428,5429,5435],{},[586,5430,5431,5433],{},[637,5432,1405],{},[1033,5434,1035],{},[593,5436,1410],{"encoding":595},[570,5438,5440,5452],{"className":5439,"ariaHidden":600},[599],[570,5441,5443,5446,5449],{"className":5442},[604],[570,5444],{"className":5445,"style":1224},[608],[570,5447,1405],{"className":5448},[765],[570,5450],{"className":5451,"style":761},[760],[570,5453,5455,5458],{"className":5454},[604],[570,5456],{"className":5457,"style":1237},[608],[570,5459,1035],{"className":5460},[613],"\" verlangen. Richtig ist der Vorzeichenwechsel ",[570,5463,5465,5491],{"className":5464},[573],[570,5466,5468],{"className":5467},[577],[579,5469,5470],{"xmlns":581},[583,5471,5472,5488],{},[586,5473,5474,5476,5478,5480,5482,5484,5486],{},[637,5475,1991],{},[637,5477,1625],{"separator":600},[637,5479,3209],{},[637,5481,1625],{"separator":600},[637,5483,1991],{},[637,5485,1625],{"separator":600},[637,5487,1628],{},[593,5489,5490],{"encoding":595},"-, +, -, \\ldots",[570,5492,5494],{"className":5493,"ariaHidden":600},[599],[570,5495,5497,5501,5504,5507,5510,5513,5516,5519,5522,5525,5528],{"className":5496},[604],[570,5498],{"className":5499,"style":5500},[608],"height:0.7778em;vertical-align:-0.1944em;",[570,5502,1991],{"className":5503},[613],[570,5505,1625],{"className":5506},[1711],[570,5508],{"className":5509,"style":1661},[760],[570,5511,3209],{"className":5512},[613],[570,5514,1625],{"className":5515},[1711],[570,5517],{"className":5518,"style":1661},[760],[570,5520,1991],{"className":5521},[613],[570,5523,1625],{"className":5524},[1711],[570,5526],{"className":5527,"style":1661},[760],[570,5529,1628],{"className":5530},[1718],[1780,5532,5533,5534,5710],{},"Das Kriterium auf nicht symmetrische Matrizen anwenden. Dann vorher mit ",[570,5535,5537,5570],{"className":5536},[573],[570,5538,5540],{"className":5539},[577],[579,5541,5542],{"xmlns":581},[583,5543,5544,5567],{},[586,5545,5546,5553,5555,5557,5559,5565],{},[5547,5548,5549,5551],"mfrac",{},[1033,5550,1622],{},[1033,5552,2352],{},[637,5554,640],{"stretchy":639},[589,5556,591],{},[637,5558,3209],{},[657,5560,5561,5563],{},[589,5562,591],{},[589,5564,667],{},[637,5566,652],{"stretchy":639},[593,5568,5569],{"encoding":595},"\\frac12(A + A^T)",[570,5571,5573,5671],{"className":5572,"ariaHidden":600},[599],[570,5574,5576,5580,5656,5659,5662,5665,5668],{"className":5575},[604],[570,5577],{"className":5578,"style":5579},[608],"height:1.1901em;vertical-align:-0.345em;",[570,5581,5583,5587,5653],{"className":5582},[613],[570,5584],{"className":5585},[696,5586],"nulldelimiter",[570,5588,5590],{"className":5589},[5547],[570,5591,5593,5644],{"className":5592},[704,1674],[570,5594,5596,5641],{"className":5595},[708],[570,5597,5600,5615,5626],{"className":5598,"style":5599},[712],"height:0.8451em;",[570,5601,5603,5606],{"style":5602},"top:-2.655em;",[570,5604],{"className":5605,"style":721},[720],[570,5607,5609],{"className":5608},[837,838,839,840],[570,5610,5612],{"className":5611},[613,840],[570,5613,2352],{"className":5614},[613,840],[570,5616,5618,5621],{"style":5617},"top:-3.23em;",[570,5619],{"className":5620,"style":721},[720],[570,5622],{"className":5623,"style":5625},[5624],"frac-line","border-bottom-width:0.04em;",[570,5627,5629,5632],{"style":5628},"top:-3.394em;",[570,5630],{"className":5631,"style":721},[720],[570,5633,5635],{"className":5634},[837,838,839,840],[570,5636,5638],{"className":5637},[613,840],[570,5639,1622],{"className":5640},[613,840],[570,5642,1698],{"className":5643},[1697],[570,5645,5647],{"className":5646},[708],[570,5648,5651],{"className":5649,"style":5650},[712],"height:0.345em;",[570,5652],{},[570,5654],{"className":5655},[756,5586],[570,5657,640],{"className":5658},[696],[570,5660,591],{"className":5661},[613,614],[570,5663],{"className":5664,"style":3454},[760],[570,5666,3209],{"className":5667},[3458],[570,5669],{"className":5670,"style":3454},[760],[570,5672,5674,5678,5707],{"className":5673},[604],[570,5675],{"className":5676,"style":5677},[608],"height:1.0913em;vertical-align:-0.25em;",[570,5679,5681,5684],{"className":5680},[613],[570,5682,591],{"className":5683},[613,614],[570,5685,5687],{"className":5686},[817],[570,5688,5690],{"className":5689},[704],[570,5691,5693],{"className":5692},[708],[570,5694,5696],{"className":5695,"style":775},[712],[570,5697,5698,5701],{"style":829},[570,5699],{"className":5700,"style":833},[720],[570,5702,5704],{"className":5703},[837,838,839,840],[570,5705,667],{"className":5706,"style":844},[613,614,840],[570,5708,652],{"className":5709},[756]," symmetrisieren, denn nur dieser Teil bestimmt die quadratische Form.",[1780,5712,5713],{},"Nur die Diagonaleinträge betrachten. Positive Diagonale ist notwendig, aber nicht hinreichend, wie das zweite Beispiel zeigt.",{"title":5715,"searchDepth":5716,"depth":5716,"links":5717},"",2,[5718,5719,5720],{"id":563,"depth":5716,"text":564},{"id":2311,"depth":5716,"text":2312},{"id":5042,"depth":5716,"text":5043},[5722,5725,5727,5729,5731,5734,5737,5739,5742,5744,5746],{"lhs":5723,"rhs":5724},"dot([x1, x2, x3], multiply([[2, -1, 0], [-1, 2, -1], [0, -1, 2]], [x1, x2, x3]))","x1^2 + (x1 - x2)^2 + (x2 - x3)^2 + x3^2",{"lhs":5726,"rhs":2352},"det([[2]])",{"lhs":5728,"rhs":2839},"det([[2, -1], [-1, 2]])",{"lhs":5730,"rhs":3090},"det([[2, -1, 0], [-1, 2, -1], [0, -1, 2]])",{"lhs":5732,"rhs":5733},"det([[1, 2], [2, 1]])","-3",{"lhs":5735,"rhs":5736},"det([[1 - x, 2], [2, 1 - x]])","(x - 3)*(x + 1)",{"lhs":5738,"rhs":4528},"dot([1, 1], multiply([[1, 2], [2, 1]], [1, 1]))",{"lhs":5740,"rhs":5741},"dot([1, -1], multiply([[1, 2], [2, 1]], [1, -1]))","-2",{"lhs":5743,"rhs":1035},"det([[0, 0], [0, -1]])",{"lhs":5745,"rhs":4376},"dot([0, 1], multiply([[0, 0], [0, -1]], [0, 1]))",{"lhs":5747,"rhs":2839},"det([[-2, 1], [1, -2]])","A \\in \\mathbb{R}^{n \\times n},\\ A^{T} = A","\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>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\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:0.9658em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7713em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">×\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>A\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A^{T} = A\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8413em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8413em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.1389em;\">T\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","symmetric-matrix-definiteness","A \\text{ positiv definit} \\iff \\vec x^{T} A\\, \\vec x > 0 \\text{ für alle } \\vec x \\neq \\vec 0 \\iff \\det A_k > 0 \\text{ für } k = 1, \\ldots, 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>\u003Cmi>A\u003C\u002Fmi>\u003Cmtext> positiv definit\u003C\u002Fmtext>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsup>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi>T\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmi>A\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmrow>\u003Cmtext> f\u003C\u002Fmtext>\u003Cmover accent=\"true\">\u003Cmtext>u\u003C\u002Fmtext>\u003Cmo>¨\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>r alle \u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmn>0\u003C\u002Fmn>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⟺\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>det\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmsub>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmrow>\u003Cmtext> f\u003C\u002Fmtext>\u003Cmover accent=\"true\">\u003Cmtext>u\u003C\u002Fmtext>\u003Cmo>¨\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>r \u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A \\text{ positiv definit} \\iff \\vec x^{T} A\\, \\vec x > 0 \\text{ für alle } \\vec x \\neq \\vec 0 \\iff \\det A_k > 0 \\text{ für } k = 1, \\ldots, 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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan 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style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\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\">A\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> f\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6679em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.25em;\">\u003Cspan class=\"mord\">¨\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">r alle \u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan 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style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2134em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⟺\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">det\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3361em;\">\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\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> f\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6679em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.25em;\">\u003Cspan class=\"mord\">¨\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">r \u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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 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