R help - Jul 2004 - QR decomposition question

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

There is N-1 linearly independent columns in the NxN matrix.

Jussi

Jussi M??kinen
Analyst, State Treasury, Finance, Finland



-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at
stat.math.ethz.ch] On Behalf Of Alex Nu
Sent: 1. hein??kuuta 2004 16:46
To: r-help at stat.math.ethz.ch
Subject: [R] QR decomposition question



 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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