On a maximum principle for inverse monotone matrices Original Research Article

Let γ = (γ1, …, γn) be a given vector with positive coordinates. A matrix A is said to satisfy the γ-maximum principle (γMP) if Ax = y, y ≥ 0 imply x ≥ 0 and image where N+) (y) is the set of indices such that y is positive. For an invertible matrix A with positive inverse the γMP is characterized geometrically by means of the behavior under A−1 of convex boundary parts of the simplex generated in (imagen+ by permissible multiples of the unit coordinate vectors. Some sufficient conditions and applications to M-matrices are given.