文献类型：期刊文献

英文题名：Some Properties of the Solution to a System of Quaternion Matrix Equations

作者：Yu, Shao-Wen[1];Zhang, Xiao-Na[2];Qin, Wei-Lu[2];He, Zhuo-Heng[2]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

年份：2022

卷号：11

期号：12

外文期刊名：AXIOMS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000900472000001)】；

基金：This research was supported by the National Natural Science Foundation of China (Grant no. 12271338, 11971294 and 11801354).

语种：英文

外文关键词：quaternion algebra; matrix decompositions; matrix equations; phi-skew-Hermicity; signature bounds

摘要：This paper investigates the properties of the phi-skew-Hermitian solution to the system of quaternion matrix equations involving phi-skew-Hermicity 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. We present the general phi-skew-Hermitian solution to this system. Moreover, we derive the beta(phi)-signature bounds of the phi-skew-Hermitian solution X-1 in terms of the coefficient matrices. We also give some necessary and sufficient conditions for the system to have beta(phi)-positive semidefinite, beta(phi)-positive definite, beta(phi)-negative semidefinite and beta(phi)-negative definite solutions.