Solving the Dual Generalized Commutative Quaternion Matrix Equation AXB = C

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB=C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB=C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB=C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.