文献类型：期刊文献

英文题名：The Solvability of a System of Quaternion Matrix Equations Involving φ-Skew-Hermicity

作者：He, Zhuo-Heng[1];Zhang, Xiao-Na[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：6

外文期刊名：SYMMETRY-BASEL

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000818301500001)】；

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 algebra; matrix decompositions; matrix equations; phi-skew-Hermicity

摘要：Let H be the real quaternion algebra and H-mxn denote the set of all m x n matrices over H. For A is an element of H-mxn, we denote by A(phi) the n x m matrix obtained by applying phi entrywise to the transposed matrix AT, where phi is a non-standard involution of H. A is an element of H-nxn is said to be phi-skew-Hermicity if A = -A phi. In this paper, we provide some necessary and sufficient conditions for the existence of a phi-skew-Hermitian solution to the system of quaternion matrix equations with four unknowns A(i)X(i)(A(i))(phi) + BiXi+1(B-i)(phi) = C-i, (i = 1,2,3), A(4)X(4)(A(4))(phi) = C-4.