On a maximum principle for inverse monotone matrices (Q1805193)

Based on the maximum principle of an \(n\times n\) matrix \(A\), the weighted maximum principle of an \(n\times n\) matrix \(A\) with respect to a fixed positive vector \(\gamma\) is introduced and discussed. For an invertible matrix \(A\) with positive inverse, the \(\gamma\)-weighted maximum principle is characterized geometrically by means of the behavior under \(A^{- 1}\) of convex boundary parts of the simplex generated in \(R^ n_ +\) by permissible multiples of the unit coordinate vectors. Sufficient conditions for the maximum principle are generalized to the \(\gamma\)- weighted maximum principle. The \(\gamma\)-weighted maximum principle for \(M\)-matrices is presented.