Determinantal Representations for the Solution of the Generalized Sylvester Quaternion Matrix Equation

Abstract

By using the determinantal representations of the Moore–Penrose inverse matrix, within the framework of the theory of noncommutative column–row determinants, we obtain determinantal representations (analogs of the Cramer rule) for the solution of the generalized Sylvester quaternion matrix equation AXB + CYD = E .