一类矩阵方程的反对称正交反对称解及其最佳逼近

The Anti-Symmetric Orthogonal Anti-Symmetric Solution of a Linear Matrix Equation and its Optimal Approximation

定义了一种新的矩阵类 :反对称正交反对称矩阵 ,研究了一类矩阵方程的反对称正交反对称解的存在性及其最佳逼近问题 .利用矩阵的广义奇异值分解 ,得到了该矩阵方程有反对称正交反对称解的充要条件及其通解表达式 ,并且给出了矩阵方程的解集合中与给定矩阵的最佳逼近 .

This paper defines a new type of matrix, i.e. anti-symmetric orthogonal anti-symmetric matrix, and studies the existence of the solution of this matrix and its optimal approximation in a typical kind of linear matrix equation.By applying the generalized singular value decomposition of matrices , we have established the necessary and sufficient conditions for the existence of solution and the general expression of the solution to this matrix, and have derived the optimal approximation of the solution in the solution set of given matrix.