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

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=Ωi,i=1,2,3,4. We design an algorithm to compute the general...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-08, Vol.12 (15), p.2341
Main Authors: He, Zhuo-Heng, Tian, Jie, Yu, Shao-Wen
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Color imagery
Control systems
Decomposition
Encryption
general solution
Image processing
matrix decomposition
quaternion matrix equation
Quaternions
solvability
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Summary: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=Ωi,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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12152341