[R] Solving Matrices

[Douglas Bates]

wettenhall at wehi.EDU.AU writes:

> On April 15th, Elizabeth wrote:
> <snip>
> >      In execises 39-42, determine if the columns of the matrix span
> >      R4:
> <snip>
> >(or x <- matrix(data=c(7, -5, 6, -7, 2, -3, 10, 9, -5,
> >                        4, -2, 2, 8, -9, 7, 15), nrow=4, ncol=4)
> >
> >That is the whole of the question <snip>
> 
> Have you tried det(x) and/or eigen(x) ?

An alternative is to determine the condition number (kappa) of the
matrix 

> x <- matrix(data=c(7, -5, 6, -7, 2, -3, 10, 9, -5, 
+                        4, -2, 2, 8, -9, 7, 15), nrow=4, ncol=4)
> kappa(x)
[1] 5.31557e+17

A very large  condition number like this indicates that the matrix is
computationally singular.