The special least squares solutions of the complex matrix equation
(AXB,CXD)=(E,F)
Abstract
In this paper, we study the problem of least square solutions of the
complex matrix equation (AXB,CXD)=(E,F). First, by using the real
representation method of the complex matrix, we prosent the real
representation form of the complex matrix equation (AXB,CXD)=(E,F). In
combination with the special structure of the real representation matrix
of the complex matrix, the vec operator of the matrix, the Kronecker
product of the matrix and the MP inverse property of the matrix, we
obtain the Hermitian least squares solution of the complex matrix
equation(AXB,CXD)=(E,F),and derive the Hermitian minimum norm least
square solution, the real symmetric minimum norm least square solution
and the real dissymmetric minimum norm least square solution of the
complex matrix equation(AXB,CXD)=(E,F). At last, we give the expressions
of three minimum norm least squares solutions and their corresponding
algorithms, respectively.