The matrix equation AXB−GXD = E over the quaternion field Original Research Article

Using the method of complex representation, this paper obtains necessary and sufficient conditions for the existence of a solution or a unique solution to the matrix equation AXB − GXD = E over the quaternion field, extends W. E. Rothʹs theorem and A. Jamesonʹs theorem to the quaternion field, and gives the representation of the solution.