文献类型：期刊文献

英文题名：A System of Four Generalized Sylvester Matrix Equations over the Quaternion Algebra

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

机构：[1]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China;[2]Shanghai Univ, Newtouch Ctr Math, Shanghai 200444, Peoples R China;[3]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2024

卷号：12

期号：15

外文期刊名：MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001287002900001)】；

基金：This research was supported by the National Natural Science Foundation of China (Grant no. 12271338 and 12371023).

语种：英文

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

摘要：In this paper, we make use of the simultaneous decomposition of eight quaternion matrices to study the solvability conditions and general solutions to a system of two-sided coupled Sylvester-type quaternion matrix equations AiXiCi+BiXi+1Di=Omega i,i=1,2,3,4. We design an algorithm to compute the general solution to the system and give a numerical example. Additionally, we consider the application of the system in the encryption and decryption of color images.