[R] How to solve A'A=S for A

Prof Brian D Ripley ripley at stats.ox.ac.uk
Fri Feb 14 18:36:04 CET 2003

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

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