反对称自正交矩阵反问题解存在的条件

基金项目:

Least-square Solutions of Inverse Problem for Symmetric Orthogonal Anti-symmetric Matrices

摘要: 讨论了一类反对称自正交矩阵的反问题,得出问题存在解的充要条件及解的表达式.并讨论了用反对称自正交矩阵构造给定矩阵的最佳逼近问题,给出了该问题有解的充要条件和解的表达式.
- 反对称自正交矩阵 /
- 矩阵范数 /
- 最佳逼近
Abstract: A kind of inverse problem for anti-symmetric and orthogonal matrices is discussed.The necessary and sufficient conditions about the problem and expression of the solution are obtained.In addition,the problem of using anti-symmetric and orthogonal matrices to construct the optimal approximation to a given matrix is discussed,the necessary and sufficient conditions about the problem are derived,and the expression of the solution are provided.
- anti-symmetric and self-orthogonal matrices /
- matrix norm /
- optimal approximation