Symmetric and skew-antisymmetric least square solutions of matrix equation A~TXA=C

By applying the generalized singular value decomposition(GSVD) of matrix pairs and the properties of symmetric and skew-antisymmetric matrix,the expression of the symmetric and skew-antisymmetric least square solutions of the matrix equation ATXA=C is given in this paper. In addition,according to the property of orthogonal matrix,the explicit expression of minimum norm solution is also derived in the corresponding symmetric and skew-antisymmetric solution set of the matrix equation.