Square nearly nonpositive sign pattern matrices Original Research Article

A sign pattern matrix A is called square nearly nonpositive if all entries but one of A2 are nonpositive. We characterize the irreducible sign pattern matrices that are square nearly nonpositive. Further we determine the maximum (resp. minimum) number of negative entries that can occur in A2 when A is irreducible square nearly nonpositive (SNNP), and then we characterize the sign patterns that achieve this maximum (resp. minimum) number. Finally, we discuss some spectral properties of the sign patterns which are square nonpositive or square nearly nonpositive.