中文摘要：

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．

英文摘要：

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.