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) with the least norm over the skew field of quaternions, and provide a numerical algorithm to calculate the forementioned solution. (C) 2007 Elsevier Ltd. All rights reserved.