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September 10, 2025Open Access

Some novel results on a classical system of matrix equations over the dual quaternion algebra

Key Points

The research establishes necessary conditions for the solvability of dual quaternion matrix equations.
It provides a general expression for solutions, including ?-Hermitian solutions for specific equations.
The solution methodology utilizes M-P inverses and ranks of quaternion matrices in the analysis.
Implications include a novel scheme for encrypting and decrypting color images, showcasing its feasibility.

Abstract

We employ the M-P inverses and ranks of quaternion matrices to establish the necessary and sufficient conditions for the solvability of a system of the dual quaternion matrix equations (AX, XC) = (B, D), along with providing an expression for its general solution. In addition, we investigate the solutions to the dual quaternion matrix equations AX = B and XC = D, including ?-Hermitian solutions. Serving as applications, we design a scheme for encrypting and decrypting color images based on this system of dual quaternion matrix equation, and experimental results show that the scheme is highly feasible.

Some novel results on a classical system of matrix equations over the dual quaternion algebra

Key Points

Abstract

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