Mv-matrices: a generalization of M-matrices based on eventually nonnegative matrices

Abstract

An M_∨ - matrix has the form A = sI − B, where s ≥ ρ(B) ≥ 0 and B is eventually nonnegative; i.e., B^k is entrywise nonnegative for all sufficiently large integers k. A theory of M_∨ - matrices is developed here that parallels the theory of M-matrices, in particular as it regards exponential nonnegativity, spectral properties, semipositivity, monotonicity, inverse nonnegativity and diagonal dominance.