M-matrix characterization II: GeneralM-matrices

Abstract

The main purpose of this paper is to provide some new characterizations of nonsingular and of singular M;-matrices. The new characterizations given here mainly relate to spectral properties and to stability. Special attention is given to a particular class of singular M-matrices which arise in many practical situations. In addition, a list of important open questions concerning the theory and applications of M-matrices is provided along with a list of references to the literature where other characterization of M-matrices can be found.