# Re: [R] rank of a matrix

From: Gabor Grothendieck <ggrothendieck_at_gmail.com>
Date: Thu 05 May 2005 - 03:48:20 EST

In this case, try a lower tolerance (1e-7 is the default):

> qr(hilbert(9), tol = 1e-8)\$rank

 9

On 5/4/05, Huntsinger, Reid <reid_huntsinger@merck.com> wrote:
> qr() returns an estimate of the rank. However the rank of a matrix isn't
> really computable (or useful) in general in finite precision arithmetic. The
> Hilbert matrix example (from help(svd)) is a good illustration:
>
> > hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
> > qr(hilbert(9))\$rank
>  7
>
> but it's actually an invertible 9 x 9 matrix.
>
> Rather you can estimate how far a matrix is from having rank <= k for
> example. A book on numerical linear algebra would be a good reference.
>
> A common approach to statistical analysis of certain kinds of data deals
> with the ranks of the data values, and that's why you got so many hits for
> "rank".
>
> Reid Huntsinger
>
> -----Original Message-----
> From: r-help-bounces@stat.math.ethz.ch
> [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of mingan
> Sent: Wednesday, May 04, 2005 11:54 AM
> To: r-help@stat.math.ethz.ch
> Subject: [R] rank of a matrix
>
> how do I check the rank of a matrix ?
>
> say
>
> A= 1 0 0
> 0 1 0
>
> then rank(A)=2
>
> what is this function?
>
> thanks
>
> I did try help.search("rank"), but all the returned help information
> seem irrelevant to what I want.
>
> I would like to know how people search for help information like this.
>
> rank(base) Sample Ranks
> SignRank(stats) Distribution of the Wilcoxon Signed Rank
> Statistic
> Wilcoxon(stats) Distribution of the Wilcoxon Rank Sum
> Statistic
> friedman.test(stats) Friedman Rank Sum Test
> kruskal.test(stats) Kruskal-Wallis Rank Sum Test
> pairwise.wilcox.test(stats)
> Pairwise Wilcoxon rank sum tests
> wilcox.test(stats) Wilcoxon Rank Sum and Signed Rank Tests
>
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