谱约束下拟自反矩阵的最佳逼近问题

Optimal Approximation Problem of Quasi-Reflexive Matrices under the Spectral Restriction

通过研究拟自反矩阵的逆特征值问题及其最佳逼近问题,建立了拟自反矩阵逆特征值问题有解的充要条件,得到了解的一般表达式.进一步,对于任意给定的n阶复矩阵,得到了相关最佳逼近问题解的表达式.

The inverse eigenvalue problem of quasi-reflexive matrices and relevant optimal approximation problem are considered. Some necessary and sufficient conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for solvable case. Furthermore, for any given complex matrix of dimension n, an expression of solution for its optimal approximation is presented.