Why x*V is different by the V*D when I use the eig function?

Hi,

I have the following x matrix. And I try to get the right eigenvectors of it using eig? It seems that when I do the product x*V=V*D the results are different. Have this to do with the fact that my matrix is not symmetric? In this case is any option of the eig function to get me the proper right eigenvectors. Thank you

x=[ [-0.308342500000000 -0.00214464000000000 0.0151461300000000 0.00824288000000000 0.00989276000000000 0.0124386100000000 0.00264512000000000 0.00866431000000000 0.0116075100000000 0.00320392000000000 0.00278671000000000 0.00149626000000000;-0.00265658000000000 -0.121676300000000 0.00564436000000000 0.00238015000000000 0.00424764000000000 0.00588706000000000 -0.000863060000000000 0.00469262000000000 0.00678557000000000 0.000689910000000000 -0.00119440000000000 -0.00716666000000000;0.0107642900000000 0.00192612000000000 -0.320937700000000 0.00805248000000000 0.0148254700000000 0.0206676400000000 -0.00345190000000000 0.00606270000000000 0.00823877000000000 0.00199755000000000 0.00131798000000000 -0.000817610000000000;0.0508680800000000 0.0185830800000000 0.101506100000000 -1.21076200000000 0.0802179500000000 0.115666400000000 -0.00754153000000000 0.0270814400000000 0.0365313200000000 0.00948934000000000 0.00735254000000000 0.000670960000000000;0.0307724700000000 0.0142414800000000 0.0643488500000000 0.0266672900000000 -0.886164400000000 0.0810198500000000 -0.00178717000000000 0.0158865000000000 0.0213394900000000 0.00575626000000000 0.00480359000000000 0.00184064000000000;0.0233513400000000 0.0135427100000000 0.0515144600000000 0.0250104400000000 0.0468383700000000 -0.613540200000000 0.00117468000000000 0.0116026500000000 0.0155001000000000 0.00438241000000000 0.00396955000000000 0.00270523000000000;0.0559105900000000 -0.0404564600000000 0.0518365000000000 0.000652430000000000 0.0562101800000000 0.0924429400000000 -1.14120900000000 0.0398392800000000 0.0555777500000000 0.0101110600000000 0.000862140000000000 -0.0283818200000000;0.0609296000000000 0.0594911000000000 0.0504506900000000 0.0286767100000000 0.0319623200000000 0.0392238000000000 0.0120725100000000 -1.39778700000000 0.107400600000000 -0.0416587600000000 0.00800827000000000 0.0169831700000000;0.0487410800000000 0.0482542000000000 0.0402743200000000 0.0229235600000000 0.0254899100000000 0.0312555200000000 0.00972080000000000 0.0492022500000000 -1.05963200000000 -0.0526606800000000 0.00732498000000000 0.0141274000000000;0.0840965800000000 0.0520060500000000 0.0734459900000000 0.0403322100000000 0.0476786100000000 0.0596631500000000 0.0137920700000000 -0.0575738400000000 -0.0862827700000000 -1.08902400000000 -0.0306083200000000 -0.00111990000000000;0.0812610900000000 0.0172178200000000 0.0751533200000000 0.0397974000000000 0.0499812100000000 0.0637146700000000 0.0101769700000000 0.0741493400000000 0.117631700000000 -0.0109123000000000 -1.12310800000000 -0.0280327400000000;0.000943080000000000 -0.000857920000000000 0.00100616000000000 0.000488290000000000 0.000705260000000000 0.000933580000000000 1.72500000000000e-05 0.000779430000000000 0.00112694000000000 0.000114870000000000 -0.000197680000000000 -0.172684800000000;]

Answer 1

[Matt J]

No, asymmetry shouldn't prevent the equation from being satisfied to within numerical precision. But I don't see a numerically significant error,

    >> [V,D]=eig(x);
    >> diff=x*V-V*D;
    >> max(abs(diff(:)))

    ans =

       1.7365e-15

[Traian Preda]

Thank you for the answer. What it will be the difference regarding the right eigenvectors if I use the svd function?

[Matt J]

It should also be small.

[Traian Preda]

No, I refeer what it is the difference between computing the right eigenvectors with the svd by comparison with the eig? Which is a more ''correct'' function?

[Matt J]

I can see how svd() could be used to get the eigenvectors of x'*x, but not of x itself.

[Traian Preda]

but then what is the V matrix from the [V,S,D]=svd(x) ?

[Matt J]

V would in that case be the left singular vectors of x, or equivalently, the eigen-vectors of x*x'. See

http://en.wikipedia.org/wiki/Singular_value_decomposition#Relation_to_eigenvalue_decomposition