一类矩阵方程的正交对称问题

Ortho-symmetric Problem of Matrix Equation

针对约束矩阵方程问题,提出了一类矩阵方程的正交对称约束问题.通过研究正交对称矩阵与对称矩阵的关系,应用矩阵的标准相关分解(CCD)原理,获得了矩阵方程正交对称约束问题存在解的充要条件,以及该问题的通解表达式,并导出了与已知矩阵最佳逼近的正交对称解,也获得了方程相应的最小范数解.

This paper put forward the ortho-symmetric problem based on the constrained matrix equation. We derived the relation between orthogonal-symmetric matrix and symmetric matrix. Using the canonical correlations decomposition （CCD） of matrix pairs, we obtained the necessary and sufficient conditions for the existence and the expression of orthogonal symmetric solutions of the constrained matrix problem. And we obtained the explicit expression of the optimal approximation solution to the given matrix and minimum norm solution in the corresponding solution set of the constrained matrix problem.