Re: Singular Values Decomposition

[w3citizen@excite.com]

On Mon, 25 Jan 1999 09:41:06 -0500 (EST), Cleve Moler wrote:

> On Sun, 24 Jan 1999 w3citizen@excite.com wrote:
> 
> > Hi,
> > 
> > I have a question concerning the SingularValuesDecomposition class. If
I
> > have a m-by-n matrix where m < n, then getU(), getS(), and getV() still
> > return the correct matrices?
> > 
> > Thanks.
> > 
> > Thomas Pham
> 
> Hi
> 
> Maybe not.  It's one of the things I should take a look at.  What is
> your experience.  To be sure, you could find the SVD of A.transpose
> and then swap U and V.
> 
>   -- Cleve Moler
> 
> 

Mr. Moler,

I didn't pay attention to the condition m >= n when I used it. That was why
I got compeletely different answer from Matlab's.

My matrix was a 4-by-5 matrix M. I used SVD to find U,S, and V such that M =
U . S . V'. If the rank of M is r, then the last n - r column vectors of V
form the null space of V. I was looking for the null space of M. Since #
rows of M < # colums of M, I got the wrong answer.

This is another problem

M = {{1,2,3}, {1,2,3}, {1,2,3}}

I used SVD to compute U,S,V such that

M = U . S . V'

When I multiplied U . S. V', I got back the original matrix M. So the
decopmposition worked correctly. But the strange thing was that U and S were
the same as from Mathlab's but V was different.

Thanks.

Thomas Pham

M is a 3-by-3 singular square matrix. 




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