The least squares Hermitian (anti)reflexive solution with the least norm to matrix equation \(A X B = C\) (Q1993353)

Summary: For a given generalized reflection matrix \(J\), that is, \(J^H = J\), \(J^2 = I\), where \(J^H\) is the conjugate transpose matrix of \(J\), a matrix \(A \in C^{n \times n}\) is called a Hermitian (anti)reflexive matrix with respect to \(J\) if \(A^H = A\) and \(A = \pm J A J \). By using the Kronecker product, we derive the explicit expression of least squares Hermitian (anti)reflexive solution with the least norm to matrix equation \(A X B = C\) over complex field.