The Solution For A Class Of Constrained Matrix Equation

In this paper, by choosing the basis of the particular matrix space, using the SVD , GSVD and vec(·), we studied the existence of (M, N)-Hermite reflexive solutions for the matrix equationsThe sufficient and necessary condition, expression of general solution and the optimal approximation solution are obtained. At last, we also discussed the existence of sufficient and necessary condition of solutions for the equation AXB = C, and the least square solution related.