Your matrix has rank 3:
A <- matrix(c(0.99252358, 0.93715047, 0.7540535, 0.4579895,
+ 0.01607797, 0.09616267, 0.2452471, 0.3088614,
+ 0.09772828, 0.58451468, 1.4907090, 1.8773815,
+ -0.01000000, 0.00000000, 0.0900000, 0.1700000),
+ byrow=TRUE, nrow=4, ncol=4)
> svdA <- svd(A)
> str(svdA)
List of 3
$ d: num [1:4] 2.78 1.11 3.48e-02 3.37e-08
$ u: num [1:4, 1:4] -0.466 -0.143 -0.871 -0.061 0.884 ...
$ v: num [1:4, 1:4] -0.198 -0.346 -0.609 -0.686 0.748 ...
The smallest singular value is 3.4e-8, which is numerically
singular relative to the largest singular value. Since you only gave us
the numbers to 8 significant digits, the smallest singular value could
be substantially smaller, e.g. 1e-16.
Hope this helps.
Spencer
p.s. I get essentially the same result using eigen(A).
On 11/20/2010 8:55 PM, Noah Silverman wrote:
Hi,
I'm trying to use the solve() function in R to invert a matrix. I get
the following error, "Lapack routine dgesv: system is exactly singular"
However, My matrix doesn't appear to be singular.
[,1] [,2] [,3] [,4]
[1,] 0.99252358 0.93715047 0.7540535 0.4579895
[2,] 0.01607797 0.09616267 0.2452471 0.3088614
[3,] 0.09772828 0.58451468 1.4907090 1.8773815
[4,] -0.01000000 0.00000000 0.0900000 0.1700000
Can anyone help me understand what is happening here?
Thanks!
-N
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--
Spencer Graves, PE, PhD
President and Chief Operating Officer
Structure Inspection and Monitoring, Inc.
751 Emerson Ct.
San José, CA 95126
ph: 408-655-4567
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