The General Solution of a System of Dual Quaternion Matrix Equations with Applications

We derive the necessary and sufficient conditions for the solvability of a system of dual quaternion matrix equations (AX, XC, EXF) = (B, D, G) as well as their general solution expressions by means of the Moore-Penrose inverse and rank equalities. Then, the main conclusions of this paper are verified via a numerical example, and the applications of such equation systems to image encryption and decryption are investigated.

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Publication Details

Journal
Symmetry
Published
2026-11-06
DOI
https://doi.org/10.3390/sym18111862
Primary Topic
Matrix Theory and Algorithms
Type
article
Field-Weighted Citation Impact
0.00

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article

The General Solution of a System of Dual Quaternion Matrix Equations with Applications

Shi-Hao Chen, Qing-Wen Wang
5 links
Symmetry
Matrix Theory and Algorithms
article

The General Solution of a System of Dual Quaternion Matrix Equations with Applications

Shi-Hao Chen, Qing-Wen Wang
article en

Abstract

We derive the necessary and sufficient conditions for the solvability of a system of dual quaternion matrix equations (AX, XC, EXF) = (B, D, G) as well as their general solution expressions by means of the Moore-Penrose inverse and rank equalities. Then, the main conclusions of this paper are verified via a numerical example, and the applications of such equation systems to image encryption and decryption are investigated.

SymmetryVol. 18(11)
National Natural Science Foundation of China
Openalex Percentile: Top 27%
Matrix Theory and Algorithms
DOIOpen Access PDFOpenAlex
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The General Solution of a System of Dual Quaternion Matrix Equations with Applications — Shi-Hao Chen, Qing-Wen Wang · Symmetry (2026) | TGRS Research Map | TGRS