Abstract: The iterative methods of the matrix equations constrained by skew-symmetric matrices and skew-anti-symmetric matrices are studied.The iterative methods are constructed and its limited convergence is proved by means of the properties of matrix’s norm and straighten operator and by using their structures and properties.Therefore,the least-norm solution and optimal approximation solution of the matrix equations are obtained.

Key words: constrained matrix equation, iterative method, least-norm solution, optimal approximation solution, skew-symmetric matrix