I'm designing a particular algorithm and part of it requires to check if a given Matrix is invertible or not. Computation of the actual determinant is not necessary.
So far I've been doing it with a LU factorization, and then checking for zeros in the diagonal of matrix U, but I was wondering if there is a computationally easier way of doing it. I need to run my algorithm many times (possibly billions) so the less steps it takes the better.
By the way, just so you know, the algorithm uses only binary matrices (their elements are only 1s and 0s) and matrices full of zeros are allowed.