The reverse order law for the generalized inverse A(2)T, S

Abstract

By using the ranks of matrices, the necessary and sufficient condition is given for the reverse order law of the generalized inverse A (2) T, S of matrix product A= A 1 A 2⋯ A n to hold. As the special cases, similar results for Moore–Penrose inverse A † , the weighted Moore–Penrose inverse A † M,N, Drazin inverse A d and group inverse A g are also derived.