Inheritance and inverse monotonicity properties of copositive matrices

A symmetric matrix A is an element of R-nxn is called copositive if it satisfies the inequality x(T) Ax >= 0 whenever x >= 0 and strictly copositive if x(T) Ax > 0, whenever 0 not equal x >= 0. The ordering of a vector here is component-wise. Certain interesting properties of the inverse of a copositive matrix are extended to its Moore-Penrose inverse. The inheritance property of the Schur complement of a copositive matrix is extended to the casewhenthe inverses in the Schur complement are replaced by their Moore-Penrose inverses. A framework is provided wherein one has the copositivity of B+ - A(+), given the copositivity of A - B.