[R] rank of a matrix

[Gabor Grothendieck]

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

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


On 5/4/05, Huntsinger, Reid <reid_huntsinger at 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
> [1] 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 at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of mingan
> Sent: Wednesday, May 04, 2005 11:54 AM
> To: r-help at 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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