[R] QR decomposition question

[Alex Nu]

 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