projection.mat <-
function(X,LinearSys,mod=1){
Y=as.matrix(LinearSys)
YY=matrix(0,nrow=nrow(Y),ncol=ncol(Y))
if (mod==1) {Y.qr=qr(Y);Y=qr.R(Y.qr)[,1:(Y.qr$rank)];}
YY[1:(Y.qr$rank),1:(Y.qr$rank)]=Y
tmp=YY%*%solve(t(YY)%*%YY)%*%t(YY)%*%X
list(projection=tmp,orth=X-tmp)#lm(X~Y)$residual...
}
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