The Anti-symmetric Orthogonal Anti-symmetric Least Squre Solutions of Matrix Equation A~TXA=B

Applying the generalized singular value decomposition (GSVD) of matrices, we obtain the expression of the anti-symmetric orthogonal anti-symmetric with a symmetric orthogonal matrix P least square solutions of the matrix equation ATXA=B(A∈Rn×m, B∈Rm×m), and derive the corresponding solution set of the equation, the explicit expressions of the optimal approximation solution to the given matrix and minimum norm solution.