文献类型：期刊文献

英文题名：A New Expression of the Hermitian Solutions to a System of Matrix Equations with Applications

作者：Song, Guangjing[1];Yu, Shaowen[2];Chen, Ming[3]

机构：[1]Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Shandong, Peoples R China;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[3]Jiaxing Univ, Coll Math Phys & Informat Engn, Jiaxing 314000, Zhejiang, Peoples R China

年份：2016

卷号：23

期号：1

起止页码：167

外文期刊名：ALGEBRA COLLOQUIUM

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000367819000018)】；

基金：This research was supported by the Post Doctoral Fund of China (2015M571539), the Doctoral Program of Shandong Province (BS2013SF011), Scientific Research Foundation of Shandong University (J141101), and Scientific Research Foundation of Weifang (2014GX027).

语种：英文

外文关键词：matrix equations; linear matrix expression; generalized inverse; inertias

摘要：In this paper, a new necessary and sufficient condition for the existence of a Hermitian solution as well as a new expression of the general Hermitian solution to the system of matrix equations A(1)X = C-1 and A(3)XB(3) = C-3 are derived. The max-min ranks and inertias of these Hermitian solutions with some interesting applications are shown. In particular, the max-min ranks and inertias of the Hermitian part of the general solution to this system are presented.