Mixed-type Reverse Order Laws for {1,3} and {1,4}-inverse of Products of two Matrices

摘要

Mixed-type reverse order laws for {1,3}-inverse and {1,4}-inverse of product of two matrices have been studied by maximal ranks and minimal ranks of Generalized Schur complement. The necessary and sufficient conditions of {AA*AB)(1,3) AA*}(c) {(AB)(1,3) and {B'B(ABB'B)(1,3)} (C) {(AB)(1,3) are obtained, similarly equivalent conditions of {AA* AB)(1,4) AA*} (C) {(AB)(1,4) and {B'B(ABB'B)(1,4)(C){(AB)(1,4)}are achieved. Especially, equivalent conditions of {B* B(ABB* B)(1,3)}={(AB)(1,3)} and {AA*AB)(1,4)AA*}={{AB(1,4)} are farther attained.