矩阵方程A^T X A=B的反对称正交反对称最小二乘解

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

通过广义奇异值分解定理.得到了矩阵方程ATXA=B的反对称正交反对称最小二乘解表达式,同时导出了相应解集中与已知矩阵最佳逼近的最小二乘解和矩阵方程的最小范数解。

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.