This study primarily investigated the equivalence conditions for the existence of solutions to two quaternion matrix systems under constraints, as well as their general solutions. As an application, it focused on studying the reducibility of solutions to classical matrix equations and their applications in image processing, such as image encryption and decryption. Finally, an example is provided to validate the main results presented in this paper.
Citation: Long-Sheng Liu, Xiao-Xiao Ma, Xiao-Quan Chen. Solutions to two systems of constrained matrix equations with an application to image processing over quaternion algebra[J]. AIMS Mathematics, 2026, 11(4): 11031-11049. doi: 10.3934/math.2026453
This study primarily investigated the equivalence conditions for the existence of solutions to two quaternion matrix systems under constraints, as well as their general solutions. As an application, it focused on studying the reducibility of solutions to classical matrix equations and their applications in image processing, such as image encryption and decryption. Finally, an example is provided to validate the main results presented in this paper.
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Long-Sheng Liu, Xiao-Xiao Ma, Xiao-Quan Chen. Solutions to two systems of constrained matrix equations with an application to image processing over quaternion algebra[J]. AIMS Mathematics, 2026, 11(4): 11031-11049. doi: 10.3934/math.2026453
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