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Asked by Ruye Wang on 20 Feb 2013

When I use [U,S,V]=svd(A), I can reproduce A by U*S*V'. However, if I generate U and V by solving two eigenvalue problems [V,D]=eig(A'*A) and [U,D]=eig(A*A'), respectively, the resulting U and V may or may NOT satisfy U*S*V'=A, due possibly to the sign difference of some of the columns (eigenvectors). While the columns of the U's and V's produced by these two different methods have the same absolute values, they may have different signs, simply because if u_i is an eigenvector of A*A', so is -u_i.

But if U*S*V'~=A for some U and V, isn't the SVD theorem violated?

Answer by Jan Simon on 20 Feb 2013

Accepted answer

I do not understand, where you see a violation. When you create U and V by another method, and consider, that they are not uniquely defined, it can be expected, that you get incompatible U and V matrices. If you want the orientation of the eigenvectors to satisfy U*S*V'=A, calculating them by solving the two separate eigenvalue problems `eig(A'*A)` and `eig(A*A')` is not sufficient.

## 1 Comment

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/64190#comment_130930

Hi, i am working on same :

http://www.mathworks.in/matlabcentral/answers/63905-is-there-any-correction