Why x*V is different by the V*D when I use the eig function?
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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;]
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Matt J
il 11 Set 2014
Modificato: Matt J
il 11 Set 2014
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
6 Commenti
Matt J
il 11 Set 2014
V would in that case be the left singular vectors of x, or equivalently, the eigen-vectors of x*x'. See
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