I have a matrix S of size m*n with column rank r. I’m looking for the null space matrix N which is a set of basis vectors for the equation SN=0. Is there any way to decompose the space of S to subspaces S_i, in which the null spaces N_i are orthogonal to each other? In other words, I’m looking for a hierarchical way to solve the equation SN=0. Can we find N_i in a way that they can form N?
Thank you so much in advance for any help on this. Best, raha