I am dealing with a large sparse integer matrix that I need to find the nullspace of. I've seen Markowitz Pivoting come up in several places discussing similar problems such as here:
And in the MAGMA documentation under the sparse null space algorithm. How can one use this technique (or similarly perhaps, the Structured Gaussian Elimination mentioned above it) to reduce a sparse matrix to a dense, small matrix? I understand that you can eliminate variables with regular Gaussian Elimination, but how does one retrieve those after solving the new system?