I am working on a modeling project where I ended up having to find the null space of a rectangular matrix computationally.
The null space was represented by a matrix who's columns were orthonormal basis vectors for the null space.
The matrix was dense, but I know due to the nature of the problem there should be a pretty nice basis for the null space.
Is there any method or algorithm that for a given matrix, it could find me the orthogonal matrix who's columns span the null space of that matrix, such that the number of 0's were maximized?
Or, if you already have a dense null space matrix, find a rotation that preserves the column space, but maximizes the 0's in the matrix?