两个矩阵乘积的加权{1,3,4}-逆的反序律

两个矩阵乘积的加权{1,3,4}-逆的反序律 The Reverse Order Law for Weighted{1,3,4}-Inverse of a Product of Two Matrices 郑胜 ZHENG Sheng 1 first-author 刘丁酉 LIU Dingyou 1 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics,Wuhan University School of Mathematics and Statistics,Wuhan University 利用广义Schur补的最大秩最小秩方法研究了两个矩阵乘积的加权{1,3,4}-逆的反序律问题,分别给出了B{1,3N,4K}A{1,3 M,4N}（AB）{1,3 M,4K},（AB）{1,3 M,4K}B{1,3N,4K}A{1,3 M,4N}和（AB）{1,3 M,4K}=B{1,3N,4K}A{1,3 M,4N}成立的等价条件. In the paper,we study the reverse order law for weighted{1,3,4}-inverse of a product of two matrices by using the expressions of maximal and minimal ranks of generalized Schur complements.Equivalent conditions for B{1,3N,4K}A{1,3 M,4N}（AB）{1,3 M,4K},（AB）{1,3 M,4K}B{1,3N,4K}A{1,3 M,4N}and B{1,3N,4K}A{1,3 M,4N}=（AB）{1,3 M,4K}to hold are presented. 加权广义逆 反序律 最大秩最小秩 广义Schur补 weighted generalized inverse reverse order law maximal and minimal ranks generalized Schur complement 10.14188/j.1671-8836.2015.04.006 O151.21 国家自然科学基金资助项目（11371284） 2015-04-01 2021-03-31 4 61