Test if matrix is invertible over finite field

Question

I would like to test if a particular type of random matrix is invertible over a finite field, in particular F_2. I can test if a matrix is invertible over the reals using

Answer 1

Unfortunately, SymPy can't yet handle finite fields in matrices, though support is planned.

As some commenters noted, though, you can just check the determinant over the integers. If it's 1 (mod 2), the matrix is invertible. To actually find the inverse, you can just take the normal inverse over the integers, multiply by the determinant (so that you don't have fractions), and mod each element by 2. I can't imagine it would be too efficient, and you could probably use any matrix library, even a numerical one (rounding to the nearest integer). SymPy can also do each of these steps.

I should point out that in general cyclic finite fields, the "multiply by the determinant" part will need to be undone by multiplying by the inverse mod p (it is unnecessary mod 2 because the only possibility is 1).