Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Bruno Luong Posts: 9,822 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

"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

Date Subject Author
12/26/12 Rick
12/26/12 Nasser Abbasi
12/26/12 Roger Stafford
12/27/12 Bruno Luong
12/27/12 Greg Heath