RE: [R] QR decomposition question

From: Mäkinen Jussi <Jussi.Makinen_at_valtiokonttori.fi>
Date: Thu 01 Jul 2004 - 23:55:20 EST


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

Jussi

Jussi Mäkinen
Analyst, State Treasury, Finance, Finland

-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Alex Nu Sent: 1. heinäkuuta 2004 16:46
To: r-help@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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R-help@stat.math.ethz.ch mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Thu Jul 01 23:59:30 2004

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