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Different Value of Eigen Vector compared with online calc.
http://forum.alglib.net/viewtopic.php?f=2&t=838		 Page 1 of 1
Author:  akunyer [ Fri May 10, 2013 7:23 am ]
Post subject:  Different Value of Eigen Vector compared with online calc.
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
Code:
SMatrixEVD(Comp, MSize, 1, True, D, Z);
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.
Author:  Sergey.Bochkanov [ Wed May 15, 2013 11:29 am ]
Post subject:  Re: Different Value of Eigen Vector compared with online cal
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).
Author:  akunyer [ Wed May 15, 2013 11:39 am ]
Post subject:  Re: Different Value of Eigen Vector compared with online cal
Thank you for your feedback. Now , i know something . I try to figure out this for a month. Thanks again.
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