Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation (Q2632533)

Summary: In this paper, we derive explicit determinantal representation formulas of general, Hermitian, and skew-Hermitian solutions to the generalized Sylvester matrix equation involving \(\ast\)-Hermicity \(\mathbf{AXA}^\ast + \mathbf{BYB}^\ast = \mathbf{C}\) over the quaternion skew field within the framework of the theory of noncommutative column-row determinants.