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

Zhuo-Heng He, Jie Tian and Shao-Wen Yu ()
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Zhuo-Heng He: Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
Jie Tian: Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
Shao-Wen Yu: School of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Mathematics, 2024, vol. 12, issue 15, 1-26

Abstract: 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 A i X i C i + B i X i + 1 D i = Ω 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.

Keywords: quaternion matrix equation; matrix decomposition; solvability; general solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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