Reverse order laws for generalized inverses of multiple matrix products

Abstract

In this article we study reverse order laws for generalized inverses and reflexive generalized inverses of the products of multiple matrices A (1),…,A (n) and the products of generalized inverses and reflexive generalized inverses of A (n),…,A (1) . By applying the multiple product singular value decomposition, we obtain necessary and sufficient conditions for one side inclusion relation of reverse order law for generalized inverses, and necessary and sufficient conditions of reverse order law for reflexive generalized inverses.