Solving homogeneous systems with sub-matrices

摘要

We show that linearly independent solutions of MX = , whereM is an m n matrix, may be found by the largest non-singular sub-matrix of M. With this method, we may also obtain eigenvectors andgeneralized eigenvectors corresponding to an eigenvalue . Finally, weshall explain how to construct a generalized modal matrix, to obtaina Jordan canonical form of a square matrix without solving a systemexcept for nding the ranks.