Square nearly nonpositive sign pattern matrices

A sign pattern matrix A is called square nearly nonpositive if all entries but one of A(2) are nonpositive. We characterize the irreducible sign patte rn matrices that are square nearly nonpositive. Further we determine the ma ximum (resp. minimum) number of negative entries that can occur in A(2) whe n A is irreducible square nearly nonpositive (SNNP), and then we characteri ze the sign patterns that achieve this maximum (resp. minimum) number. Fina lly, we discuss some spectral properties of the sign patterns which are squ are nonpositive or square nearly nonpositive. (C) 2001 Elsevier Science Inc . All rights reserved.