Two special kinds of least squares solutions for the quaternion matrix equation AXB + CXD = E

Abstract

By using the complex representation of quaternion matrices, the Moore-Penrose generalized inverse and the Kronecker product of matrices, the expressions of the least squares η-Hermitian solution with the least norm and the expressions of the least squares η-anti-Hermitian solution with the least norm are derived for the matrix equation AXB+CXD = E over quaternions.