The consistency and the exact solutions to a system of matrix equations

被引：9

作者：

Farid, F. O. ^{[1
]}

He, Zhuo-Heng ^{[1
]}

Wang, Qing-Wen ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2016年 / 64卷 / 11期

基金：

中国国家自然科学基金;

关键词：

matrix equation; generalized inverses; Moore-Penrose inverse; rank; inertia; GENERALIZED SYLVESTER EQUATIONS; OPERATOR-EQUATIONS; HERMITIAN SOLUTIONS; POSITIVE SOLUTIONS; ASTERISK; PAIR; INERTIA; RANKS; AX;

D O I：

10.1080/03081087.2016.1140717

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide two techniques, which establish criteria for the consistency of a system of matrix equations (see (1.1)). The system encompassesmatrix systems that were not studied before. We present the solutions set of a consistent system (1.1), using each technique. We investigate the link between the two techniques. We study the number of solutions that a system (1.1) could have, and establish a necessary and sufficient condition for a consistent system (1.1) to have a unique solution. If A(i), B-i and C-i, i = 1, ..., s, are all the zero matrices in (1.1) and the system is consistent, we provide bounds for the rank and inertia of any Hermitian solution of the system.

引用

页码：2133 / 2158

页数：26

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