[R] matrix inverstion

[Petr Savicky]

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.