文献类型：期刊文献

英文题名：Consistency and General Solutions to Some Sylvester-like Quaternion Matrix Equations

作者：He, Zhuo-Heng[1];Tian, Jie[1];Zhao, Yun-Fan[2];Yu, Shao-Wen[3]

机构：[1]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China;[2]Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA;[3]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2022

卷号：14

期号：7

外文期刊名：SYMMETRY-BASEL

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000834458500001)】；

基金：This research was supported by the National Natural Science Foundation of China (grant nos. 11801354 and 11971294).

语种：英文

外文关键词：quaternion matrix equation; matrix decomposition; consistency; general solution

摘要：This article makes use of simultaneous decomposition of four quaternion matrixes to investigate some Sylvester-like quaternion matrix equation systems. We present some useful necessary and sufficient conditions for the consistency of the system of quaternion matrix equations in terms of the equivalence form and block matrixes. We also derive the general solution to the system according to the partition of the coefficient matrixes. As an application of the system, we present some practical necessary and sufficient conditions for the consistency of a phi-Hermitian solution to the system of quaternion matrix equations in terms of the equivalence form and block matrixes. We also provide the general phi-Hermitian solution to the system when the equation system is consistent. Moreover, we present some numerical examples to illustrate the availability of the results of this paper.