Why x*V is different by the V*D when I use the eig function?
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Traian Preda
el 11 de Sept. de 2014
Comentada: Matt J
el 11 de Sept. de 2014
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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Respuesta aceptada
Matt J
el 11 de Sept. de 2014
Editada: Matt J
el 11 de Sept. de 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 comentarios
Matt J
el 11 de Sept. de 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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