A system of dual quaternion matrix equations with its applications

TL;DR

This paper develops methods to solve dual quaternion matrix equations using M-P inverses and ranks, providing conditions, solutions, and applications including Hermitian solutions, validated through a numerical example.

Contribution

It introduces necessary and sufficient conditions for solving dual quaternion matrix equations and explores their solutions, including special cases like Hermitian solutions.

Findings

Established conditions for solving dual quaternion matrix equations

Derived explicit general solutions for the equations

Validated results with a numerical example

Abstract

We employ the M-P inverses and ranks of quaternion matrices to establish the necessary and sufficient conditions for solving a system of the dual quaternion matrix equations $(AX, XC) = (B, D)$, along with providing an expression for its general solution. Serving as an application, we investigate the solutions to the dual quaternion matrix equations $AX = B$ and $XC=D$, including $\eta$-Hermitian solutions. Lastly, we design a numerical example to validate the main research findings of this paper.