拟复广义正定矩阵上的Oppenheim不等式的推广

首先改进了关于Hermitian正定矩阵的Hadamard乘积的行列式的下界估计的经典的Oppenheim不等式的加强形式,然后应用这个结论和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阵的Hadamard乘积的行列式的模的新下界估计.这些结果不仅推广和改进了有关拟复广义正定矩阵的Hadamard乘积的行列式的模的下界估计的文献,而且概括了关于实正定矩阵和亚正定矩阵Hadamard乘积的行列式的下界估计的Oppenheim型不等式.

Generalization of Oppenheim Type Inequality for quasi -generalized complex positive definite matrices

The strengthened form of the classical Oppenheim Type Inequality for estimating the lower bound of the determinant on the Hadamard product of Hermitian positive definite matrices is improved. Furthermore, a new estimation of the lower bound of the determinant module on the Hadamard product of a Hermitian positive definite matrix and a quasi-generalized complex positive definite matrix is obtained by using the improvement and the properties of quasi-generalized complex positive definite matrices. These results not only generalize and improve the corresponding results on quasi-generalized complex positive definite matrices in the recent relevant papers, but also summarize the classical Oppenheim Type Inequality for estimating the lower bound of the determinant on the Hadamard product of real positive definite matrices and metapositive definite matrices.