文献类型：期刊文献

英文题名：The Solution of a Generalized Sylvester Quaternion Matrix Equation and Its Application

作者：Song, Guang-Jing[1];Yu, Shaowen[2]

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

年份：2017

卷号：27

期号：3

起止页码：2473

外文期刊名：ADVANCES IN APPLIED CLIFFORD ALGEBRAS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000408268200031)】；

基金：This research was supported by the Post Doctoral Fund of China (2015M571539), the Doctoral Program of Shan Dong Province (BS2013SF011), Scientific Research of Foundation of Shan Dong University (J14LI01), Scientific Research of Foundation of Weifang 2014GX027) and Shanghai Natural Science Foundation (17ZR1407800)

语种：英文

外文关键词：Moore-Penrose inverse; Generalized Sylvester matrix equation; eta-Hermitian matrix

摘要：An n x n quaternion matrix is said to b eta-Hermitian if A = A eta*, where A eta* = -eta A*eta, eta is one of the quaternion units i, j, k, and A* is the conjugate transpose of A. In this paper, we investigate the generalized Sylvester quaternion matrix equation A(1)X(1)B(1) + A(2)X(2)B(2) + A(3)X(3)B(3) = C. We establish the necessary and sufficient conditions for the existence of a solution to this equation, and give an expression of the general solution to the equation when it is solvable. As an application, we derive the solvability conditions for the quaternion matrix equation A(1)X(1)A(1)(eta)* + A(2)X(2)A(2)(eta)* + A(3)X(3)A(3)(eta)* = C to have an eta-Hermitian solution as well as an expression of the eta-Hermitian solution.