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

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Dale D. Olesky
Michael J. Tsatsomeros
Pauline van den Driessche


An M - matrix has the form A = sI − B, where s ≥ ρ(B) ≥ 0 and B is eventually nonnegative; i.e., Bk 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.

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