Return eigenvalues and eigenvectors of a matrix
Details
Standardization depends on what you need to perform factor analysis. We implemented two types:
pca_weighted_eigen: This is the default method in FactoMineR to compute eigvalues, eigvectors and U matrix.pca_eigen: This is the standard method to compute eigenvalues, eigenvectors.
Examples
library(FactoMineR2)
iris[, -5] |>
pca_standardize_norm() |>
pca_eigen()
#> $values
#> [1] 434.856175 136.190540 21.866774 3.086511
#>
#> $vectors
#> Dim.1 Dim.2 Dim.3 Dim.4
#> Sepal.Length 0.5210659 -0.37741762 0.7195664 0.2612863
#> Sepal.Width -0.2693474 -0.92329566 -0.2443818 -0.1235096
#> Petal.Length 0.5804131 -0.02449161 -0.1421264 -0.8014492
#> Petal.Width 0.5648565 -0.06694199 -0.6342727 0.5235971
#>
#> $U
#> [,1] [,2] [,3] [,4]
#> [1,] -0.1082395313 -0.0409957970 0.027218646 0.013710648
#> [2,] -0.0994577561 0.0575731483 0.050003401 0.058435855
#> [3,] -0.1129963029 0.0292000319 -0.009420891 0.016098333
#> [4,] -0.1098970995 0.0510193897 -0.019457133 -0.037416661
#> [5,] -0.1142204597 -0.0552417975 -0.003354363 -0.020379051
#> [6,] -0.0992030036 -0.1271804935 -0.005747892 0.003748828
#> [7,] -0.1168102651 -0.0040689659 -0.071500545 -0.020862814
#> [8,] -0.1067170177 -0.0190575546 0.018904131 -0.013962469
#> [9,] -0.1115821423 0.0952525283 -0.030920984 -0.015237265
#> [10,] -0.1043980945 0.0400552488 0.054086370 -0.022634909
#> [11,] -0.1035369360 -0.0891344989 0.057265395 0.009491723
#> [12,] -0.1111754327 -0.0113653128 -0.019983394 -0.075725286
#> [13,] -0.1060289608 0.0622312605 0.049215308 0.001375727
#> [14,] -0.1258467928 0.0821157306 -0.038534006 -0.010900993
#> [15,] -0.1050869241 -0.1588547893 0.100791840 0.110471545
#> [16,] -0.1081206062 -0.2294172328 -0.006506294 0.028667844
#> [17,] -0.1055097633 -0.1267049550 0.001139014 0.107116335
#> [18,] -0.1046858790 -0.0417483459 0.009423839 0.052810307
#> [19,] -0.0907406226 -0.1199930706 0.079785722 0.034659809
#> [20,] -0.1119993170 -0.0963219219 -0.028268219 -0.021419258
#> [21,] -0.0914934282 -0.0349175769 0.089792273 0.006195658
#> [22,] -0.1054822888 -0.0789229070 -0.034072915 0.033809630
#> [23,] -0.1325974291 -0.0391440060 -0.070799052 0.011146576
#> [24,] -0.0869217526 -0.0073069701 -0.007350733 0.085742453
#> [25,] -0.1064453629 -0.0117219667 -0.025148574 -0.153250916
#> [26,] -0.0932868238 0.0534298158 0.065142846 0.024712572
#> [27,] -0.0980330233 -0.0206815371 -0.018407209 0.038394972
#> [28,] -0.1036452889 -0.0450202449 0.044079818 0.005829242
#> [29,] -0.1022586028 -0.0267497965 0.057791656 0.047800348
#> [30,] -0.1082662331 0.0288433780 -0.014586072 -0.061427297
#> [31,] -0.1022853047 0.0430893785 0.015986938 -0.027337597
#> [32,] -0.0875395035 -0.0361849054 0.057646113 0.136078728
#> [33,] -0.1249791972 -0.1531770786 -0.010066038 -0.130045793
#> [34,] -0.1169129535 -0.1836789964 0.017619469 -0.027352078
#> [35,] -0.1008444422 0.0393026999 0.036291563 0.016464749
#> [36,] -0.1055203356 0.0176022268 0.048049532 0.095821620
#> [37,] -0.0977460115 -0.0564991653 0.103271968 0.111394405
#> [38,] -0.1207916644 -0.0505836854 -0.004142455 -0.077439180
#> [39,] -0.1161222082 0.0772198492 -0.041189367 -0.005524618
#> [40,] -0.1036994653 -0.0229631179 0.037487030 0.003998001
#> [41,] -0.1092801213 -0.0377238980 -0.007437333 0.060691714
#> [42,] -0.0888073715 0.1996226835 0.043529498 0.164440117
#> [43,] -0.1220489602 0.0409167217 -0.065169588 -0.037783077
#> [44,] -0.0938890947 -0.0403381986 -0.065986933 0.100465059
#> [45,] -0.1021389050 -0.0975500093 -0.052949932 -0.085687106
#> [46,] -0.0989216563 0.0607261627 0.013625695 0.079575044
#> [47,] -0.1139762794 -0.0956882576 -0.012195139 -0.086360793
#> [48,] -0.1144371654 0.0329867105 -0.029725517 -0.027704013
#> [49,] -0.1065544885 -0.0852289357 0.038682496 -0.008468747
#> [50,] -0.1053303317 -0.0007871062 0.032615968 0.028008637
#> [51,] 0.0526586881 -0.0737005873 0.145909396 0.019761239
#> [52,] 0.0349536459 -0.0507819874 0.020060649 0.002781831
#> [53,] 0.0593115438 -0.0526337785 0.118078347 0.005345903
#> [54,] 0.0194753038 0.1498316767 0.004923799 0.037310732
#> [55,] 0.0514013923 0.0177998198 0.084882263 0.059417342
#> [56,] 0.0185769784 0.0506683081 -0.026469588 -0.136623859
#> [57,] 0.0356797497 -0.0660183061 -0.031750621 -0.043891963
#> [58,] -0.0232911731 0.1582033316 -0.053127198 -0.022987157
#> [59,] 0.0443482642 -0.0027522095 0.127064665 -0.016950735
#> [60,] 0.0005461049 0.0883084471 -0.114858419 -0.016146060
#> [61,] -0.0052667368 0.2266662541 0.009972690 0.007806478
#> [62,] 0.0210625660 0.0054056103 -0.043708445 0.022763570
#> [63,] 0.0268654851 0.1507130709 0.163212825 0.025943335
#> [64,] 0.0343908442 0.0159041732 0.014633637 -0.093495303
#> [65,] -0.0015941595 0.0374922694 -0.041547057 0.061863332
#> [66,] 0.0418393370 -0.0434756799 0.107315989 0.059534688
#> [67,] 0.0167399785 0.0167656461 -0.104622322 -0.108643470
#> [68,] 0.0075901902 0.0676474939 0.064374748 -0.116465628
#> [69,] 0.0585523010 0.1385447768 0.102795955 0.128153185
#> [70,] 0.0078821098 0.1112469683 0.036837818 -0.029344698
#> [71,] 0.0352569104 -0.0338684718 -0.131403446 -0.047247173
#> [72,] 0.0227637384 0.0356404784 0.056470641 0.064427405
#> [73,] 0.0589864852 0.0797089836 0.078521616 -0.005641540
#> [74,] 0.0302469157 0.0355608348 0.062213361 -0.155565391
#> [75,] 0.0335830895 0.0054155709 0.095064047 0.024653955
#> [76,] 0.0417851606 -0.0214185528 0.100723201 0.057703448
#> [77,] 0.0600537772 0.0065979096 0.154982313 0.022515340
#> [78,] 0.0649238094 -0.0282950706 0.055591320 0.037911633
#> [79,] 0.0317735642 0.0192949569 -0.018300615 -0.020672361
#> [80,] -0.0019241258 0.0904179288 0.068112319 0.036754391
#> [81,] 0.0062512434 0.1334229800 0.031966756 -0.005334061
#> [82,] 0.0011209012 0.1342944135 0.051483289 -0.018591843
#> [83,] 0.0115441149 0.0663801654 0.032228588 0.013417442
#> [84,] 0.0507141081 0.0541322276 -0.022445561 -0.104365504
#> [85,] 0.0107048737 0.0245767726 -0.141788119 -0.144564410
#> [86,] 0.0205103365 -0.0722154109 -0.096045974 -0.062218849
#> [87,] 0.0501230591 -0.0445848827 0.084356003 0.021108717
#> [88,] 0.0499224830 0.1181116322 0.146700084 0.077626985
#> [89,] 0.0033259142 0.0187462824 -0.062145801 -0.083475281
#> [90,] 0.0135485518 0.1135285492 -0.019056421 0.005052273
#> [91,] 0.0133382833 0.0956539957 -0.020138632 -0.153544122
#> [92,] 0.0298507783 -0.0021285059 0.004365253 -0.083782656
#> [93,] 0.0160841808 0.0844128445 0.042496972 0.003704795
#> [94,] -0.0173102447 0.1724493321 -0.022554188 0.011102543
#> [95,] 0.0137927321 0.0730820891 -0.027897197 -0.060929469
#> [96,] 0.0043665043 0.0154743834 -0.027489822 -0.130456346
#> [97,] 0.0108835326 0.0328733983 -0.033294519 -0.075227458
#> [98,] 0.0275479846 0.0132266974 0.057898249 -0.011266985
#> [99,] -0.0213958618 0.1318447464 -0.040581137 0.113429843
#> [100,] 0.0122702186 0.0511438467 -0.019582682 -0.033256352
#> [101,] 0.0881595893 -0.0743367465 -0.214286328 -0.027939433
#> [102,] 0.0553399601 0.0596857075 -0.112995779 -0.022987468
#> [103,] 0.1053988377 -0.0479974810 0.043248148 0.033575257
#> [104,] 0.0688307676 0.0040128894 -0.034875332 -0.133752619
#> [105,] 0.0892704855 -0.0251977657 -0.084322325 -0.009246027
#> [106,] 0.1315234294 -0.0683574897 0.124110556 -0.057515529
#> [107,] 0.0175412961 0.1333573099 -0.210341675 -0.075521296
#> [108,] 0.1100431214 -0.0358749356 0.138901570 -0.135041056
#> [109,] 0.0959078612 0.0607591222 0.083973252 -0.049077575
#> [110,] 0.1080041231 -0.1640603917 -0.084732296 0.059475232
#> [111,] 0.0651995994 -0.0591636030 -0.060660846 0.061189334
#> [112,] 0.0765986545 0.0360145587 -0.004941839 0.033091599
#> [113,] 0.0900394207 -0.0358052527 -0.005613642 0.083061354
#> [114,] 0.0602261220 0.0992607340 -0.123671537 0.056252056
#> [115,] 0.0701448455 0.0377713992 -0.213959923 0.156381596
#> [116,] 0.0759963837 -0.0577534557 -0.136071618 0.108844086
#> [117,] 0.0703258066 -0.0218309163 -0.007977918 -0.088119032
#> [118,] 0.1159643160 -0.2183469966 0.027256038 -0.155331113
#> [119,] 0.1582318602 -0.0015185496 0.149899103 0.025635545
#> [120,] 0.0604006459 0.1457614800 0.057021524 -0.036977139
#> [121,] 0.0973909055 -0.0777568105 -0.050044030 0.095278929
#> [122,] 0.0467417517 0.0488304906 -0.176503041 0.015745775
#> [123,] 0.1384907715 -0.0353262612 0.182746756 -0.072238136
#> [124,] 0.0637206901 0.0411482094 0.001156975 0.079398977
#> [125,] 0.0812851201 -0.0865921500 -0.063610325 -0.034970557
#> [126,] 0.0934053712 -0.0860674097 0.089513520 -0.123863584
#> [127,] 0.0561630717 0.0270210935 -0.027694307 0.071151154
#> [128,] 0.0487954572 -0.0054953554 -0.071979154 -0.004909651
#> [129,] 0.0854726529 0.0160012432 -0.057686743 0.017636056
#> [130,] 0.0890714388 -0.0480214151 0.152526807 -0.118120689
#> [131,] 0.1164243223 -0.0221437147 0.155123226 -0.010167944
#> [132,] 0.1101620465 -0.2242963714 0.105176629 -0.120083860
#> [133,] 0.0890263052 0.0152486943 -0.075481550 0.056735715
#> [134,] 0.0532497371 0.0250165230 0.039107832 -0.105712982
#> [135,] 0.0574711817 0.0692889027 0.035108428 -0.277684505
#> [136,] 0.1337648367 -0.0731737275 0.115712475 0.167853641
#> [137,] 0.0753358013 -0.0912602228 -0.201594725 0.020199186
#> [138,] 0.0643448781 -0.0360769168 -0.038550928 -0.122208731
#> [139,] 0.0442012149 -0.0014709075 -0.088840326 0.002971755
#> [140,] 0.0885169072 -0.0577434950 0.002700873 0.110734472
#> [141,] 0.0962961390 -0.0524277845 -0.091292798 0.140428754
#> [142,] 0.0908941419 -0.0588919389 -0.027723560 0.266459419
#> [143,] 0.0553399601 0.0596857075 -0.112995779 -0.022987468
#> [144,] 0.0975267330 -0.0740890166 -0.072070383 0.025634706
#> [145,] 0.0954997292 -0.0896023456 -0.134789552 0.121428077
#> [146,] 0.0893991030 -0.0330481333 -0.054620974 0.220825832
#> [147,] 0.0747777843 0.0765799034 0.005620663 0.124915218
#> [148,] 0.0727030413 -0.0229793601 -0.038402352 0.067605916
#> [149,] 0.0656112167 -0.0863643414 -0.198939364 0.014822811
#> [150,] 0.0459137323 0.0020780018 -0.112588405 -0.092514345
#>