Some properties of matrices with signed null spaces

A matrix A is said to have signed null space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null space of à is S for each Ã∈Q(A). It is a generalization of a number of important qualitative matrix classes such as L-matrices, S∗-matrices, totally L-matrices, etc. In this paper, we obtain some new characterizations for matrices with signed null spaces. As applications, these results are used to obtain di3erent proofs of some known properties and characterizations of matrices with signed null spaces, and are further used to study some special classes of matrices with signed null spaces. c © 2003 Elsevier B.V. All rights reserved.