Re: Possible bug in Jama!

[Cleve Moler <moler@mathworks.com>]

On Fri, 7 Jan 2000, Vijay S. Rajan wrote:

> Dear Sirs,
> 
> I am using Jama for a class project. I am getting erroneous left and right
> singular vectors when I use svd.
> I need to know the problem and how to fix this.
> 
> for example
> 
> if I do svd  on the matrix
> 1.44  3.08
> 3.92  1.44
> and then a getU
> I get 
> 0.6  0.8
> 0.8 -0.6
> 
> whereas the correct answer should be
> 
> 
> 0.6 -0.8
> 0.8  0.6
> 
> The same can be said about right singular vectors
> Please help ASAP.
> Thanx
> Vijay S Rajan
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>            Goleta, CA, 93117
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> 
> 
> 
Hi --

In the SVD, the signs of the columns of U are not uniquely
determined.  You can change the sign of all the elements in
any column if you also change the sign of the corresponding
column of V.  The definining relationship, A = U*S*V', 
still holds.  More generally, if you have repeated singular
values, you can take linear combinations of the corresponding
columns and still have a valid SVD.

  -- Cleve Moler
  moler@mathworks.com