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

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. Serving as applications, 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.