[R] QR decomposition question

From: Alex Nu <notulei_at_yahoo.com>
Date: Thu 01 Jul 2004 - 23:46:28 EST

 Hi all,

 I wonder if this kind of questions are ok in this list...

 Quick question:

 What does it mean than the rank of the QR  decomposition of a NxN matrix is N-1 ?

  m: NxN matrix
  qr(m)$rank equal to (N-1)

 Long version:
 I'm doing a manova on a matrix of 10 variables  and 16 observations.

> dim(tmp)

[1] 16 10
> fit <- manova( tmp ~ treatment*mouse )

>results <- summary(fit,test="Wilks")

...
residuals have rank 9 < 10

So the QR decomposition returns with a rank  of 9. What does this mean ?

 Does this necessarily mean a linear dependency  among the columns of the matrix ?

 Thanks

 Alex



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