关于Oppenheim定理的推广

Generalization of Oppenheim's Theorem

首先给出了拟复广义正定矩阵类(CP)_(D_n)的定义,这个矩阵类包含了复正定矩阵和复广义正定矩阵类,然后应用拟复广义正定矩阵的性质,得到了Hermitian正定矩阵和拟复广义正定矩阵的Hadamard乘积的行列式的模的下界估计,这些结果不仅概括了经典的关于Hermitian正定矩阵的Hadamard乘积的行列式的下界估计的Oppenheim定理,而且也推广和改进了最近有关复广义正定矩阵的Hadamard乘积的行列式的模的下界估计文献。

In the paper, the definition of the similar complex generalized positive matrix (CP)Dn is given firstly. This matrix type contains the complex positive definite matrix and the complex generalized positive definite matrix. Then the application of the characteristics of the similar complex generalized positive definite matrix gives rise to the lower bound estimation of the determinant modulo about the Hadamard product of Hermi-tian positive definite matrix and similar complex generalized positive definite matrix. These not only gather up the classical oppemiheirm theorem about the lower bound estimation of the determinant modulo about the Hadamard product of the Hermitian positive definite matrix, but also extend and improve the recent literature on the lower bound estimate of the determinant modulo about the Hadamard product of the complex generalized positive definite matrix.