半正定Hermitian矩阵伪Schur补的商公式  

The quotient formulas on generalized Schur complements of positive semidefinite Hermitian matrices

作　　者：楼嫏嬛 LOU Lang-huan(School of Science,Xiʹan University of Posts&Telecommunications,Xiʹan 710121,China)

机构地区：[1]西安邮电大学理学院,陕西西安710121

出　　处：《云南大学学报（自然科学版）》2020年第3期401-410,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：陕西省教育厅自然科学专项基金(17JK0695).

摘　　要：利用半正定Hermitian矩阵及其伪Schur补的性质研究半正定Hermitian矩阵伪Schur补的商性质.通过分块矩阵的计算与比对,将矩阵Schur补的商公式推广到半正定Hermitian矩阵的伪Schur补上.并以此为基础,得出半正定Hermitian矩阵伪Schur补的{1}广义逆也满足商公式以及其Moore-Penrose广义逆满足商公式的条件.The quotient properties on generalized Schur complements of positive semidefinite Hermitian matrices are studied with the properties of positive semidefinite Hermitian matrices and their generalized Schur complements.The quotient formulas on Schur complements are extended to generalized Schur complements of positive semidefinite Hermitian matrices by computing and comparing the block matrices.Based on this,the quotient formulas on some{1}generalized inverses involving generalized Schur complements of positive semidefinite Hermitian matrices are also obtained.The condition under which the quotient formula on MoorePenrose generalized inverse satisfies is derived.

关 键 词：伪Schur补 半正定Hermitian矩阵 主子矩阵 广义逆 

分 类 号：O151.21[理学—数学]