A new equivalent condition of the reverse order law for reflexive generalized inverses of two matrix products

Abstract

Let C mxn denote the set of m x n matrices with complex entries and C m denote the set of m -dimensional vectors. I k denotes the identity matrix of order k , O mxn be the m x n matrix of all zero entries (if no confusion occurs, we will drop the subscript). For a matrix A ∈ C mxn , A * and r(A) denote the conjugate transpose and the rank of the matrix A , respectively. © 2012 Springer-Verlag London Limited.