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

被引：0
|
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.
引用
收藏
页数：26
相关论文
共 50 条
  • [1] A Constraint System of Generalized Sylvester Quaternion Matrix Equations
    Abdur Rehman
    Qing-Wen Wang
    Ilyas Ali
    Muhammad Akram
    M. O. Ahmad
    [J]. Advances in Applied Clifford Algebras, 2017, 27 : 3183 - 3196
  • [2] A Constraint System of Generalized Sylvester Quaternion Matrix Equations
    Rehman, Abdur
    Wang, Qing-Wen
    Ali, Ilyas
    Akram, Muhammad
    Ahmad, M. O.
    [J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2017, 27 (04) : 3183 - 3196
  • [3] A system of generalized Sylvester quaternion matrix equations and its applications
    Zhang, Xiang
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2016, 273 : 74 - 81
  • [4] A System of Matrix Equations over the Quaternion Algebra with Applications
    Nie, Xiangrong
    Wang, Qingwen
    Zhang, Yang
    [J]. ALGEBRA COLLOQUIUM, 2017, 24 (02) : 233 - 253
  • [5] Three Methods for Solving Generalized Sylvester Matrix Equations Over Boolean Algebra
    Hashemi, Behnam
    Shirazi, Mahsa Nasrollahi
    Tavakolipour, Hanieh
    [J]. JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, 2015, 25 (4-5) : 427 - 445
  • [6] The η-Anti-Hermitian Solution to a System of Constrained Matrix Equations over the Generalized Segre Quaternion Algebra
    Ren, Bai-Ying
    Wang, Qing-Wen
    Chen, Xue-Ying
    [J]. SYMMETRY-BASEL, 2023, 15 (03):
  • [7] The reducible solution to a system of matrix equations over the Hamilton quaternion algebra
    Liu, Long-Sheng
    Wang, Qing-Wen
    [J]. FILOMAT, 2023, 37 (09) : 2731 - 2742
  • [8] Solving a System of Sylvester-like Quaternion Matrix Equations
    Wang, Ruo-Nan
    Wang, Qing-Wen
    Liu, Long-Sheng
    [J]. SYMMETRY-BASEL, 2022, 14 (05):
  • [9] A System of Coupled Two-sided Sylvester-type Tensor Equations over the Quaternion Algebra
    Wang, Qing-Wen
    Wang, Xiao
    [J]. TAIWANESE JOURNAL OF MATHEMATICS, 2020, 24 (06): : 1399 - 1416
  • [10] Solving the system of generalized Sylvester matrix equations over the generalized centro-symmetric matrices
    Dehghan, Mehdi
    Hajarian, Masoud
    [J]. JOURNAL OF VIBRATION AND CONTROL, 2014, 20 (06) : 838 - 846
12345