A System of Four Generalized Sylvester Matrix Equations over the Quaternion Algebra

被引：3
|
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
来源：
MATHEMATICS | 2024年 / 12卷 / 15期
基金：
中国国家自然科学基金;
关键词：
quaternion matrix equation; matrix decomposition; solvability; general solution; PAIR;
D O I：
10.3390/math12152341
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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页数：26
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