inverse of a matrix with Fraction entries

[Mark Wooding]

Daniel Fetchinson <fetchinson at googlemail.com> writes:

> So after all I might just code the inversion via Gauss elimination
> myself in a way that can deal with fractions, shouldn't be that hard.

I wouldn't do it that way.  Let M be your matrix.  Work out the LCM l of
the denominators, and multiply the matrix by that to make it an integer
matrix N = l M.  Then work out the determinant d of that integer matrix.
Next, the big step: use Gaussian elimination to find a matrix A (the
`adjugate matrix') such that A N = d I.  This should be doable entirely
using integer arithmetic, and I think without needing any divisions.
Finally, we have l A M = d I, so (l/d A) M = I and l/d A is the inverse
you seek.

Does that make sense?

-- [mdw]