两个矩阵乘积{1,2,3}-逆和{1,2,4}-逆的混合反序律

Mixed-type reverse order laws for {1,2,3}-inverse and {1,2,4}-inverse of products of two matrices

利用了广义Schur补的最大秩与最小秩,研究了两个矩阵乘积的{1,2,3}-逆和{1,2,4}-逆的混合反序律.得到了单边包含关系{B(1,2,3)(ABB(1,2,3))(1,2,3)}■{(AB)(1,2,3)}与{A(1,2,3)AB)(1,2,3)A(1,2,3)}■{(AB)(1,2,3)}成立的充要条件,以及{B(1,2,4)(ABB(1,2,4))(1,2,4)}■{(AB)(1,2,4)}与{A(1,2,4)AB)(1,2,4)A(1,2,4)}■{(AB)(1,2,4)}成立的等价条件.

Mixed-type reverse order laws for {1,2,3}-inverse and {1,2,4}-inverse of product of two matrices were studied by use of maximal and minimal ranks of generalized Schur complement.The necessary and sufficient conditions of unilateral inclusion relation {B（1,2,3）（ABB（1,2,3））（1,2,3）}■{（AB）（1,2,3）} and {A（1,2,3）AB）（1,2,3）A（1,2,3）}■{（AB）（1,2,3）} were obtained,similarly equivalent conditions of {B（1,2,4）（ABB（1,2,4））（1,2,4）}■{（AB）（1,2,4）} and {A（1,2,4）AB）（1,2,4）A（1,2,4）}■{（AB）（1,2,4）} were achieved.