The Least-Norm Solution to a Matrix Equation over the Dual Quaterion Algebra

In this paper, we explore the least-norm solution to the classical matrix equation AXB=C over the dual quaternion algebra, where A, B, and C are given matrices, while X remains the unknown matrix. We begin by transforming the definition of the Frobenius norm for dual quaternion matrices into an equivalent form. Using this new expression, we investigate the least-norm solution to the equation AXB=C under solvability conditions. Additionally, we examine the minimum real part of the norm solution in cases where a least-norm solution does not exist. Finally, we provide two numerical examples to illustrate the main findings of our study.