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Matrix decomposition: orthogonal complement

3 messages · Florin G. Maican, Brian Ripley, Simon Wood

Original
Florin G. Maican
# 
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
Brian Ripley
#
On Tue, 2 Nov 2004, Florin G. Maican wrote:

            

      
      
      
    

        
It is far from unique, of course.

            

      
      
      
    

        
library(MASS)
?Null

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Simon Wood
    

    

      
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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