Given two matrices, A and B, each with n rows, and with p and q columns, respectively, a very common goal is the comparison of these matrices in a subspace of dimension s, 1 ≤ s ≤ min p, q. That is, assuming linear mappings of A and B into the subspace, the comparison involves the choice of two transformation matrices L and M of dimensions p by s and q by s, respectively, and the subsequent comparisons of the images AL and BM in some fashion.