Hello, 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. I need to compute A_. How I can compute A_ in R? Best Regards, /Florin -- Florin G. Maican Ph.D. candidate, Department of Economics School of Economics and Commercial Law Gothenburg University, Sweden E-mail: Florin.Maican at handels.gu.se P.O.Box 640 SE-405 30 Gothenburg, Sweden Phone no +46 31 773 4866 Fax no +46 31 773 4154
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?library(MASS) ?Null -- 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
> How I can compute in R the orthogonal complement of one matrix?use the qr decomposition. For example: A<-matrix(rnorm(40),10,4) B <- t(qr.Q(qr(A),complete=TRUE)[,5:10]) B%*%A best, Simon> > 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. > > I need to compute A_. How I can compute A_ in R? > > Best Regards, > /Florin > > -- > Florin G. Maican > Ph.D. candidate, Department of Economics > School of Economics and Commercial Law > Gothenburg University, Sweden > E-mail: Florin.Maican at handels.gu.se > P.O.Box 640 SE-405 30 Gothenburg, Sweden Phone no +46 31 773 4866 > Fax no +46 31 773 4154 > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html >