REVERSE ORDER LAW FOR REFLEXIVE GENERALIZED INVERSES OF PRODUCTS OF MATRICES

The relationships between generalized inverses of the product of two m atrices A; B and the product of generalized inverses of A, B have been studied in the literature. By applying the product singular value dec omposition (P-SVD), in this paper we derive equivalent conditions for B{1,2}A{1,2} subset of or equal to (AB){1,2}, (AS){1,2}subset of or eq ual to B{1,2}A{1,2}, B{1,2}A{1,2} = (AB){1,2}, and equivalent conditio ns for (AB){1} subset of or equal to B{1} A{1}, (C) 1998 Elsevier Scie nce Inc. All rights reserved.