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Research Article | Open Access

Solutions to two systems of constrained matrix equations with an application to image processing over quaternion algebra

Long-Sheng Liu( ), Xiao-Xiao Ma, Xiao-Quan Chen
School of Mathematics and Statistics, Anqing Normal University, Anqing 246011, China
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Abstract

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.

Keywords

image processingmatrix equationrankMoore-Penrose
CLC number: 15A24, 15A23, 15A33

References

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 11031-11049
DOI: 10.3934/math.2026453

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Liu L-S, Ma X-X, Chen X-Q. Solutions to two systems of constrained matrix equations with an application to image processing over quaternion algebra. AIMS Mathematics, 2026, 11(4): 11031-11049. https://doi.org/10.3934/math.2026453

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Received: 05 February 2026
Revised: 02 April 2026
Accepted: 13 April 2026
Published: 21 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)