Reverse order law for reflexive generalized inverses of products of matrices Original Research Article

The relationships between generalized inverses of the product of two matrices A. B and the product of generalized inverses of A, B have been studied in the literature. By applying the product singular value decomposition (P-SVD), in this paper we derive equivalent conditions for B{1, 2}A{1, 2} subset of or equal to (AB){1, 2}, (AB){1, 2} subset of or equal to B{1, 2}A{1, 2}, B{1, 2}A{1, 2} = (AB){1, 2}, and equivalent conditions for (AB){1} subset of or equal to B{1} A{1}.