Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations (Q1728872)

Summary: Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer's rule) of solutions and Hermitian solutions to the system of two-sided quaternion matrix equations \(\mathbf{A}_1 \mathbf{X} \mathbf{A}_1^\ast = \mathbf{C}_1\) and \(\mathbf{A}_2 \mathbf{X} \mathbf{A}_2^\ast = \mathbf{C}_2\). Since the Moore-Penrose inverse is a necessary tool to solve matrix equations, we use determinantal representations of the Moore-Penrose inverse previously obtained by the theory of row-column determinants.