forum.alglib.net

Hi ,
I need to use the value from eigen vector to do Rotated Factor Loading . When i verified the calculation with the online matrix calculator from Bluebit , it seems that the value is correct but some of the eigen vector value was -(ve) and some are totally reversal. Below is the example of the symmetric metrics

1.000 0.440 0.615 0.383 0.224 0.469 0.357 0.373
0.440 1.000 0.485 0.545 0.374 0.373 0.311 0.533
0.615 0.485 1.000 0.540 0.543 0.471 0.441 0.416
0.383 0.545 0.540 1.000 0.758 0.236 0.357 0.441
0.224 0.374 0.543 0.758 1.000 0.184 0.384 0.367
0.469 0.373 0.471 0.236 0.184 1.000 0.363 0.525
0.357 0.311 0.441 0.357 0.384 0.363 1.000 0.745
0.373 0.533 0.416 0.441 0.367 0.525 0.745 1.000

Using the online calculator , the results below


( 0.332, 0.000i) ( 0.253, 0.000i) (-0.515, 0.000i) ( 0.225, 0.000i) (-0.473, 0.000i) (-0.461, 0.000i) ( 0.158, 0.000i) (-0.220, 0.000i)
( 0.354, 0.000i) (-0.040, 0.000i) (-0.165, 0.000i) (-0.789, 0.000i) (-0.189, 0.000i) ( 0.300, 0.000i) (-0.158, 0.000i) (-0.269, 0.000i)
( 0.394, 0.000i) (-0.049, 0.000i) (-0.331, 0.000i) ( 0.367, 0.000i) (-0.017, 0.000i) ( 0.675, 0.000i) ( 0.082, 0.000i) ( 0.368, 0.000i)
( 0.373, 0.000i) (-0.495, 0.000i) (-0.022, 0.000i) (-0.097, 0.000i) ( 0.056, 0.000i) (-0.453, 0.000i) (-0.351, 0.000i) ( 0.524, 0.000i)
( 0.334, 0.000i) (-0.575, 0.000i) ( 0.124, 0.000i) ( 0.219, 0.000i) ( 0.274, 0.000i) (-0.011, 0.000i) ( 0.298, 0.000i) (-0.574, 0.000i)
( 0.307, 0.000i) ( 0.489, 0.000i) (-0.168, 0.000i) (-0.007, 0.000i) ( 0.755, 0.000i) (-0.126, 0.000i) (-0.208, 0.000i) (-0.095, 0.000i)
( 0.344, 0.000i) ( 0.217, 0.000i) ( 0.575, 0.000i) ( 0.303, 0.000i) (-0.303, 0.000i) ( 0.096, 0.000i) (-0.523, 0.000i) (-0.195, 0.000i)
( 0.383, 0.000i) ( 0.266, 0.000i) ( 0.472, 0.000i) (-0.206, 0.000i) (-0.026, 0.000i) (-0.105, 0.000i) ( 0.643, 0.000i) ( 0.304, 0.000i)

But , using the alglib in Delphi , this is the results

(-0.15803252231, -0.22021778579, 0.46109942579, -0.47291068586, -0.22460107131, -0.51535611476, 0.25279078065, 0.3321624699),
(0.15779676545, -0.26887558606, -0.30016916815, -0.18864093336, 0.78946861249, -0.16468825077, -0.04008187139, 0.35373676982),
(-0.081898521277, 0.3684230306, -0.67508012766, -0.017132298394, -0.36684025758, -0.33113721908, -0.049083662629, 0.39357028591),
(0.35141070993, 0.52353033783, 0.4531406666, 0.055748426016, 0.096908097212, -0.021995319777, -0.49509791966, 0.37280722115),
(-0.29831265882, -0.57430671768, 0.010864459917, 0.27409319384, -0.21945938891, 0.12433846992, -0.57484154243, 0.33447116293),
(0.20849364692, -0.094717109294, 0.12642431992, 0.75499540937, 0.0065775843066, -0.16830314089, 0.48866523402, 0.30723764218),
(0.52318437655, -0.19525135567, -0.09551516869, -0.30257239057, -0.30261214293, 0.57506099386, 0.21727767568, 0.34351560838),
(-0.64323177221, 0.30408530593, 0.10484204755, -0.02595149694, 0.20627873794, 0.47187821955, 0.26554286024, 0.3826051442)

I'm stuck now , I need to know why some of the values are different ( seems like (-ve) value ) ? any explanation regarding this. How can i customize the functions to have similar results like the online calculator. Thanks.

Eigenvectors are non-unique. If x is eigenvector of A, then -x is also eigenvector of A, and there is no way to say that one of these eigenvectors is "right", and other is "wrong".

Furthermore, if A has duplicate eigenvalues, eigenvectors will become even "more non-unique" (you can find something about it in Wikipedia).

Thank you for your feedback. Now , i know something . I try to figure out this for a month. Thanks again.