Least squares Hermitian solution of the matrix equation (AXB,CXD)=(E,F) with the least norm over the skew field of quaternions

By using the complex representations of quaternion matrices, Moore–Penrose generalized inverse and the Kronecker product of matrices, we derive the expression of the least squares Hermitian solution of the matrix equation (AXB,CXD)=(E,F)(AXB,CXD)=(E,F) with the least norm over the skew field of quaternions, and provide a numerical algorithm to calculate the forementioned solution.