R help - Feb 2003 - How to solve A'A=S for A

It is not clear to me that one can. If the singular value decomposition
of A is the triple product P d Q', then the singular value decomposition
of A'A=S is Q d^2 Q'. The information about the orthonormal matrix P is
lost, is it not?
**********************************************************
Cliff Lunneborg, Professor Emeritus, Statistics &
Psychology, University of Washington, Seattle
Visiting: Melbourne, Feb-May 1999, Brisbane, Jun-Aug 1999,
Sydney, Sep-Nov 1999, Perth, Dec 1999-Feb 2000
cliff at stat.washington.edu

Well, you cannot solve uniquely for A, there is an orthogonal solution,
a triangular solution, a symmetric solution and so on. It is true that
the solution is unique up to an orthonormal tranformation.

On Friday, Feb 14, 2003, at 08:51 US/Pacific, Cliff Lunneborg wrote:
> It is not clear to me that one can. If the singular value decomposition
> of A is the triple product P d Q', then the singular value  
> decomposition
> of A'A=S is Q d^2 Q'. The information about the orthonormal matrix
P is
> lost, is it not?
> **********************************************************
> Cliff Lunneborg, Professor Emeritus, Statistics &
> Psychology, University of Washington, Seattle
> Visiting: Melbourne, Feb-May 1999, Brisbane, Jun-Aug 1999,
> Sydney, Sep-Nov 1999, Perth, Dec 1999-Feb 2000
> cliff at stat.washington.edu
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> http://www.stat.math.ethz.ch/mailman/listinfo/r-help
>
>
==Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
Editor: Journal of Multivariate Analysis, Journal of Statistical  
Software
US mail: 9432 Boelter Hall, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550;  fax (310)-206-5658;  email: deleeuw at stat.ucla.edu
homepage: http://gifi.stat.ucla.edu
   
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On Fri, 14 Feb 2003, Cliff Lunneborg wrote:
> It is not clear to me that one can. If the singular value decomposition
> of A is the triple product P d Q', then the singular value
decomposition
> of A'A=S is Q d^2 Q'. The information about the orthonormal matrix
P is
> lost, is it not?
S was a covariance matrix, so symmetric and non-negative definite.
Hence P = Q.
> **********************************************************
> Cliff Lunneborg, Professor Emeritus, Statistics &
> Psychology, University of Washington, Seattle
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595