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 A X B = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation A X B = 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 A X B = 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. [ABSTRACT FROM AUTHOR]

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