On matrices satisfying a maximum principle with respect to a cone Original Research Article

A matrix equation Ax = y is considered in the space imagen that is ordered by a cone K. In case image it is known that a matrix A is said to satisfy the maximum principle if A is invertible and for each image the solution x belongs to imagen+ and is such that xi = max1 less-than-or-equals, slant k less-than-or-equals, slant nxk and yi > 0 for some i. This concept is generalized to finitely generated and to circular cones image. This is achieved by “evaluating” x and y with the aid of elements of a given base for the polar cone Kring operator of K. The maximum principle is characterized geometrically by means of the behavior under A−1 of convex boundary parts of a base for K. A weighted maximum principle is investigated and an infinite dimensional example is indicated.