Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products

Abstract

This paper considers how to construct and describe matrix equalities that are composed of algebraic operations of matrices and their generalized inverses. We select a group of known and new reverse-order laws for generalized inverses of several matrix products and derive various necessary and sufficient conditions for them to hold using the matrix rank method and the block matrix method.

Keywords

• generalized inverse
• matrix product
• matrix equality
• reverse-order law
• set inclusion
• rank