文献类型：期刊文献

英文题名：On Solvability of Hermitian Solutions to a System of Five Matrix Equations

作者：Yu, Shao-wen[1];Song, Guang-jing[2]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[2]Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Shandong, Peoples R China

年份：2014

卷号：11

期号：2

起止页码：237

外文期刊名：MEDITERRANEAN JOURNAL OF MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000335233600002)】；

基金：This research was supported by the National Natural Science Foundation of China (11226067), the Fundamental Research Funds for the Central Universities (WM1214063), China Postdoctoral Science Foundation (2012M511014).

语种：英文

外文关键词：System of Matrix equations; minimal rank; maximal rank; Hermitian solution; generalized inverse

摘要：In this paper, we establish the formulas of the maximal and minimal ranks of the Hermitian matrix expression where X (1) and X (2) are Hermitian solutions to two systems of matrix equations A (1) X (1) = C (1),X (1) B (1) = C (2) and A (2) X (2) = C (3),X (2) B (2) = C (4), respectively. Using this result and matrix rank method, we give necessary and sufficient conditions for the existence of Hermitian solutions to a system of five matrix equations by rank equalities. The general expressions and extreme ranks of the Hermitian solutions X (1) and X (2) to the system mentioned above are also presented.