埃尔米特广义汉密尔顿矩阵的广义逆特征值问题

Generalized Inverse Eigenvalue Problem for Hermitian Generalized Hamiltonian Matrices

本文利用埃尔米特广义汉密尔顿矩阵的性质与矩阵的分解理论,导出了埃尔米特广义汉密尔顿矩阵的广义逆特征值问题解的一般表达式。进而运用希尔伯特空间的逼近理论,对任意给定的n阶复矩阵对,证明相关最佳逼近解的存在性与惟一性,得到了最佳逼近解的表达式。

By means of properties of Hermitian generalized Hamiltonian matrices and the matrix decomposition theory,we derive expressions of the generalized inverse eigenvalue problem for Hermitian generalized Hamiltonian matrices.By using the Hilbert space approximation theory,for any given square complex matrices,we prove that there is only one optimal approximation solution,and furthermore derive expressions of the optimal approximation solution.