Re: Singular Values Decomposition

[Cleve Moler <moler@mathworks.com>]

:On Mon, 25 Jan 1999 w3citizen@excite.com wrote:

> 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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