[R] Matrix decomposition: orthogonal complement

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Nov 2 15:08:20 CET 2004

On Tue, 2 Nov 2004, Florin G. Maican wrote:

> How I can compute in R the orthogonal complement of  one matrix?
> If  A (n x m ) matrix of full column rank (n>m), its orthogonal 
> complement is denoted by A_ .
> A_  is  n X (n-m) matrix of full column rank and such that A'A_=0.

It is far from unique, of course.

> I  need to compute A_.   How I can compute A_ in R?


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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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