[R] Two ?'s:Permuting a data matrix and projection operator

[Stephane Dray]

>
>2.  Is there a function which helps find a matrix... projection operator
>from p dimensional to p-1 dimensional subspace orthogonal to x, a real
>number?

I don't really understand what dou you want...
The expression of the projection operator on subspace engendered by a 
matrix X is:
PX=X%*%(t(X)%*%Dn%*%X)-%*%t(X)%*%Dn
where Dn is a diagonal matrix of row weight and (t(X)%*%Dn%*%X)- is 
generalized inverse of (t(X)%*%Dn%*%X).
In multivariate regression analysis you use:
y=PX%*%y+error=a+bX1+cX2+...+error
But if you want a regression without term a (i.e. orthogonal to 
vector (1,1,...1), you must centered matrix X.

Is it what you want ?
-- 
Stéphane DRAY
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Biométrie et Biologie évolutive - Equipe "Écologie Statistique"
Universite Lyon 1 - Bat 711 - 69622 Villeurbanne CEDEX - France

Tel : 04 72 43 27 56			   Fax : 04 78 89 27 19
       04 72 43 27 57 	   E-mail : dray at biomserv.univ-lyon1.fr 
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ADE-4               http://pbil.univ-lyon1.fr/ADE-4/ADE-4F.html
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