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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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Roger Stafford

Posts: 5,886
Registered: 12/7/04
Re: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Posted: Dec 26, 2012 11:39 PM
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"Rick" wrote in message <kbgbi5$g5n$1@newscl01ah.mathworks.com>...
> 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. But when I use the command schur(),
> it seems that S appears negative real numbers on the diagonal as the following. Is there any problem?

- - - - - - - - - -
Unless your A matrix is positive definite there is no reason its singular value and schur decompositions should be the same, and the A you have defined is certainly not positive definite. In fact all its eigenvalues are negative. Check the Wikipedia site:

http://en.wikipedia.org/wiki/Schur_decomposition

Roger Stafford



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