On Mon, Mar 28, 2011 at 04:51:00PM +0200, Rosario Garcia Gil wrote:
> Hello
>
> I have this matrix which I am trying to invert. I get a message about
> reciprocal condition number, what that does mean?
>
> > XT_X
> [,1] [,2] [,3] [,4] [,5]
> [1,] 3 0 0 2 1
> [2,] 0 2 0 1 1
> [3,] 0 0 2 1 1
> [4,] 2 1 1 4 0
> [5,] 1 1 1 0 3
> > iXT_X <- solve(XT_X)
> Error in solve.default(XT_X) :
> system is computationally singular: reciprocal condition number =
> 1.11022e-17
This matrix is exactly singular. For example, the sum of
the first three rows is equal to the sum of the last two.
cbind(1, 1, 1, -1, -1) %*% XT_X
[,1] [,2] [,3] [,4] [,5]
[1,] 0 0 0 0 0
For matrices with small integer entries, a test for
singularity may be done using det().
det(XT_X)
[1] 8.881784e-15
Since the exact determinant is an integer, it has to be zero
and the difference from zero is due to rounding error.
Hope this helps.
Petr Savicky.
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