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Output of Gauss and the matrix A in R with 2 respectively 3 chebyshev dimensions
Matrix A with 2 Chebyshev dimensions
0.02512,-0.004737,0.007601,-0.04078, -0.6924, -0.7038, 0.0211, 0.1069, 0.08342,
-0.4515, -1.702, -1.86, 0.9796, 21.03, 20.92, -0.609, -4.458, -4.45,
0.603, 2.267, 2.472, -1.238, -26.91, -26.75, 0.6754, 3.956, 3.954,
-0.08095, -0.2813, -0.3053, 0.1189, 2.771, 2.747,-0.0006015, 0.7651, 0.7647,
0.003696, -0.2972, -0.2867, 0.05323, 1.626, 1.576,-0.07115, -0.929, -0.9989,
0.01021, 0.3455, 0.3393,-0.07593, -2.139, -2.085, 0.07575, 0.8628, 0.9324,
-0.1153, -0.5003, -0.5348, 0.2221, 5.071, 5.026, -0.0905, -0.1657, -0.1841,
0.08565, 0.1868, 0.2132,-0.08094, -1.91, -1.899,-0.07192, -1.812, -1.834,
-0.074, -0.1387, -0.1614, 0.05732, 1.385, 1.377, 0.08377, 1.87, 1.892,
Eigenvalues
0.3065
0.08797
0.04888
-4.851e-014
1.396e-014
-1.654e-016 + 1.293e-016i,
-1.654e-016 - 1.293e-016i,
1.628e-017 + 7.145e-017i,
1.628e-017 - 7.145e-017i,
Eigenvectors
0.01245,-0.2611,-0.1346,5.113,5.257,0.6738 + 0.1535i, 0.6738 - 0.1535i, -3.344 + 8.267i, -3.344 - 8.267i,
1.948,0.5281,-0.9838,-10.26,-41.71,-1.795 - 2.509i, -1.795 + 2.509i, -4.582 + 0.03152i, -4.582 - 0.03152i,
-2.579,-0.5023,0.4631,34.34,48.17,2.105 + 2.993i, 2.105 - 2.993i, 4.048 + 2.613i, 4.048 - 2.613i,
0.3084,-0.01688,0.5149,-19.5,-0.3362,0.05323 - 2.271i, 0.05323 + 2.271i, 5.579 - 7.742i, 5.579 + 7.742i,
0.3663,-0.6723,-0.8055,21.01,5.329,-0.0746 - 0.1589i, -0.0746 + 0.1589i, -0.2167 + 0.04262i, -0.2167 - 0.04262i,
-0.4198,0.6681,0.7446,-17.87,-4.306,0.1378 + 0.2922i, 0.1378 - 0.2922i, -0.0201 + 0.7933i, -0.0201 - 0.7933i,
0.569,-0.1342,0.07387,-11.1,-3.728,0.1909 - 2.562i, 0.1909 + 2.562i, 6.848 + 1.124i, 6.848 - 1.124i,
-0.1849,-0.1484,-1.113,36.12,-1.125,0.01991 + 0.2006i, 0.01991 - 0.2006i, -0.5958 + 0.4346i, -0.5958 - 0.4346i,
0.13,0.1515,1.119,-34.61,1.778,-0.001076 - 0.03496i,-0.001076 + 0.03496i, 0.1683 - 0.3048i, 0.1683 + 0.3048i,
Matrix A with 3 Chebyshev dimensions
0.01367, -0.1108, -0.1059, 0.05055, 1.1, 1.085, -0.1165, -1.75, -1.78, 0.0774, 1.954, 1.959,
-0.704, -3.136, -3.399, 1.929, 40.65, 40.46, -1.672, -17.22, -17.27, -0.3893, -8.491, -8.624,
0.8066, 3.397, 3.684, -1.969, -42.1, -41.87, 1.469, 13.34, 13.38, 0.3503, 7.944, 8.083,
-0.108, -0.4369, -0.4722, 0.2229, 4.917, 4.883, -0.1189, -0.6646, -0.6718,-0.01463, -0.3876, -0.4027,
0.1831, 0.7265, 0.8106, -0.6175, -12.27, -12.25, 0.6765, 8.022, 7.999, 0.3398, 7.548, 7.602,
-0.1727, -0.7023, -0.7839, 0.6131, 12.12, 12.11, -0.6959, -8.396, -8.374, -0.341, -7.54, -7.594,
-0.1062, -0.4694, -0.5019, 0.2165, 4.89, 4.849, -0.1058, -0.4742, -0.4917, 0.03068, 0.663, 0.6512,
-0.05197, -0.424, -0.4433, 0.2374, 5.058, 5.022, -0.2832, -3.502, -3.542, 0.0543, 1.483, 1.476,
0.06157, 0.4611, 0.4834, -0.2542, -5.441, -5.402, 0.2881, 3.48, 3.52,-0.05492, -1.487, -1.479,
-0.03742, -0.1441, -0.1551, 0.06134, 1.422, 1.409,-0.01088, 0.2061, 0.2033, 0.00716, 0.121, 0.1171,
0.05359, 0.2043, 0.2186,-0.07171, -1.764, -1.744,-0.01599, -0.7523, -0.7467,-0.02835, -0.5648, -0.5608,
-0.05402, -0.2116, -0.2264, 0.07896, 1.903, 1.882,0.003759, 0.5815, 0.5753, 0.02613, 0.5246, 0.5203,
Eigenvalues
0.3222
0.07881
0.1022
2.129e-013
-4.042e-014
2.078e-014
8.074e-016 + 1.554e-016i,
8.074e-016 - 1.554e-016i,
5.674e-017
-2.229e-017 + 5.318e-017i,
-2.229e-017 - 5.318e-017i,
-4.333e-018
Eigenvector
0.172,-0.6496,-0.1543,7.924,-17.25,4.248,-0.4509 - 1.725i, -0.4509 + 1.725i, 2.573,-0.4093 - 1.032i, -0.4093 + 1.032i, -2.206
3.66,-0.7498, 2.206, -106.6, -32.11, 12.57, -4.349 - 9.674i, -4.349 + 9.674i, -0.1785 -0.03499 - 0.2026i,-0.03499 + 0.2026i, 0.4826
-3.805, 0.264, -1.687, 112.8, 5.252, -13.68,-0.8503 + 1.846i, -0.8503 - 1.846i, -0.1847,0.07899 + 0.2367i, 0.07899 - 0.2367i, 0.1095
0.4592,-0.002936,0.01923, -11.73, 2.861, 3.537, 1.046 - 0.09125i, 1.046 + 0.09125i, -0.1136, 1.174 - 0.2905i, 1.174 + 0.2905i, 0.2065
-0.9536,-0.3371, -1.748, 51.34, 9.581, 10.95,-0.2695 - 1.625i, -0.2695 + 1.625i, 0.09265 -0.08932 - 0.07889i,-0.08932 + 0.07889i, -0.0226
0.9408, 0.2784, 1.789, -49.71, -12.68, -11.2,-0.2669 + 0.8498i, -0.2669 - 0.8498i, -0.0631, 0.0438 + 0.09791i, 0.0438 - 0.09791i,0.007234
0.4895,-0.1833,-0.1664, -7.141,0.09841, 6.444, 1.065 - 0.8949i, 1.065 + 0.8949i,-0.05325, 0.6567 + 1.605i, 0.6567 - 1.605i, -0.5409
0.5399,-0.8048,0.01194,-0.9941, -22.34, 5.696,-0.5944 - 0.3434i, -0.5944 + 0.3434i, 0.06997 -0.07897 - 0.1058i,-0.07897 + 0.1058i,-0.04414
-0.5766, 0.8007,-0.0002701, 1.903, 21.16, -6.081, 0.3777 + 0.1566i, 0.3777 - 0.1566i,-0.03359,0.04326 - 0.007052i, 0.04326 + 0.007052i, 0.04775
0.1391,0.01316,-0.07249, -2.709, 2.486, 1.975, 0.7292 - 0.4287i, 0.7292 + 0.4287i, 0.4506,-0.4887 + 0.4212i, -0.4887 - 0.4212i, 1.556
-0.1845,-0.009119, 0.2069, 1.978, -4.494, -3.864, -1.908 + 0.2664i, -1.908 - 0.2664i, -0.1228,0.01069 + 0.1218i, 0.01069 - 0.1218i, 0.01264
0.1969,-0.008204,-0.1861, -2.431, 3.823, 3.625, 1.734 - 0.4579i, 1.734 + 0.4579i, 0.08133,0.01722 - 0.1376i, 0.01722 + 0.1376i,-0.05036
A.2.chebdim <- structure(c(0.0251195687410812, -0.451487019043338, 0.602969317133404,
-0.080946015318336, 0.00369570592651655, 0.010209124169268, -0.115344772782954,
0.0856517687037747, -0.074004961413312, -0.00473711505721341,
-1.70171807889158, 2.26672172167781, -0.281338931397627, -0.297198751092101,
0.34552768893191, -0.500308766008281, 0.186797467880112, -0.13870136788775,
0.00760091658427825, -1.86009613220146, 2.47161434444769, -0.305316480872239,
-0.28666744331867, 0.33933915427856, -0.534781130802257, 0.213196719674662,
-0.161383000086935, -0.0407788435223874, 0.9795723352226, -1.23792951757023,
0.118871533636273, 0.0532315672820695, -0.0759279989560321, 0.222057579557723,
-0.0809371702401839, 0.0573154452330507, -0.692374678424168,
21.0293936228799, -26.9063230129794, 2.77098758691049, 1.62570726197241,
-2.13939525889925, 5.07090486018187, -1.91031780606037, 1.38453257847103,
-0.703796065857319, 20.9231836480967, -26.7534858782059, 2.74682926509546,
1.57550882010931, -2.08544093485461, 5.02589337095768, -1.89897321983338,
1.37704518557191, 0.0210992067868763, -0.608997435005441, 0.675435086527622,
-0.00060153238132792, -0.0711490418360262, 0.0757453950671834,
-0.0905044724103719, -0.0719159035403148, 0.0837703469087769,
0.106937584030175, -4.45790092817428, 3.95626116997033, 0.765075016328704,
-0.929033813289299, 0.86277682485081, -0.165724899155797, -1.81241067225944,
1.86961557767679, 0.0834222097904443, -4.45038720484062, 3.95419836274529,
0.764742212409605, -0.998914908111172, 0.93240875059386, -0.184051565617139,
-1.83384622123727, 1.89213240310663), .Dim = c(9L, 9L))
A.3.chebdim <- structure(c(0.0136674091348247, -0.703976734974693, 0.806593644171027,
-0.107985641966237, 0.183058233590881, -0.172741342802184, -0.106202990263937,
-0.0519650216187242, 0.0615680527054799, -0.0374153128626347,
0.0535929452971758, -0.05401880697326, -0.110775450072092, -3.13576233232038,
3.39689417867967, -0.436901055459487, 0.726471846908179, -0.702333086786863,
-0.469361964448975, -0.424047897349256, 0.46113888532498, -0.144062699382402,
0.204325492937412, -0.211583856125461, -0.105911164460766, -3.39853008011693,
3.68390739159443, -0.472195193865039, 0.810573938407148, -0.78385619715199,
-0.501856386572946, -0.443342644895591, 0.483363089680578, -0.15508702265143,
0.218627330747033, -0.226379571624227, 0.0505533095586058, 1.92870074075039,
-1.96923515889548, 0.222902142358754, -0.617531487591071, 0.613073389516368,
0.216465695507199, 0.237353023142707, -0.254170157690672, 0.0613392762777892,
-0.0717121432338294, 0.0789567120185122, 1.10001107976705, 40.6483575742824,
-42.0969604451543, 4.91653471457016, -12.2661091781262, 12.1194611596901,
4.88970467127651, 5.05804111015103, -5.44107533632013, 1.4219880430752,
-1.76440077939546, 1.90310768963979, 1.08494308175366, 40.4566118108628,
-41.874452320835, 4.88323541307331, -12.2539602608117, 12.1099195314376,
4.84861378035628, 5.02215855359606, -5.40206050389266, 1.40914921094934,
-1.74361668797602, 1.88219709037991, -0.116511836862127, -1.67217845520115,
1.46927946049909, -0.118883664990999, 0.676538542208269, -0.695877927423144,
-0.105775868202838, -0.283186771776859, 0.288081561865589, -0.0108797879982163,
-0.0159938069079269, 0.00375891489057329, -1.74997596395904,
-17.2165835034171, 13.3353506345884, -0.66455704164009, 8.02241118275611,
-8.39630986131621, -0.474244517788, -3.5020633960178, 3.4796019557024,
0.206120242942166, -0.752346084859653, 0.581537529593852, -1.7801252342435,
-17.2718706115357, 13.3819223846476, -0.671792675357825, 7.99885474375042,
-8.37421184562738, -0.491686412915189, -3.54167636101464, 3.51982086639232,
0.203309289268448, -0.746654095776618, 0.57528514232418, 0.0774000640648815,
-0.389313793273199, 0.350288990932256, -0.0146265237746175, 0.339780682663692,
-0.341006524591558, 0.0306783371943635, 0.0543009883069646, -0.0549155421056335,
0.0071602703068457, -0.0283531470166062, 0.0261298444911918,
1.95420444129994, -8.49088398964678, 7.94425615025396, -0.38763048780306,
7.54764449853665, -7.54049490946318, 0.662986752439449, 1.48283403726504,
-1.48739212225965, 0.120982609506016, -0.564766741884512, 0.524605272592779,
1.95872657194325, -8.62380144451482, 8.08270375947611, -0.402749216455236,
7.60173266910818, -7.59383504180384, 0.651213105610295, 1.47562948475477,
-1.47906403705416, 0.117052947019585, -0.560846666948256, 0.520283887551588
), .Dim = c(12L, 12L))
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