Semipositivity of matrices

Abstract

A real m×n matrix A is semipositive provided there is an x≥0 in such that Ax≥0. Semipositivity plays roles in the study of M-matrices, in convergence theory for sets of matrices, and in linear programming. This paper investigates properties associated with semipositivity, characterizes inverse nonegative matrices as matrices possessing an appropriately defined "minimal" semipositivity, and relates semipositivity of a general rectangular matrix with that of its square submatrices.