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Topic: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Replies: 4   Last Post: Dec 27, 2012 7:30 PM

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Bruno Luong

Posts: 8,819
Registered: 7/26/08
Re: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Posted: Dec 27, 2012 2:22 AM
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"Rick" wrote in message <kbgbi5$g5n$1@newscl01ah.mathworks.com>...
> Hi everyone,
> as we know, for a real symmetric matrix A, A, there exists a singular value decomposition as A=USU', and S should be a rectangular diagonal matrix with nonnegative real numbers on the diagonal.


It is a wrong statement, as Roger has pointed it out.

Take an extreme case where A is 1x1. Any matrix is symmetric, the svd is: U = V = 1, and S = A(1,1). There is no reason for A(1,1) to be positive.

Bruno



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