| By applying the generalized singular-value decomposition (GSVD) of matrix pairs and the properties of symmetric and skew-antisymmetric , we obtain the sufficient and necessary conditions under which the matrix equation AXAT = C is solvable in n × n symmetric and skew-antisymmetric matrix set, and prove that if the above equation is solvable, then there exists a unique minimal norm solution, and give the procedure to find this solution, where A ∈ Rm×n and C ∈ Rm×m are given matrices. |
