一个行列式不等式的进一步研究

FURTHER ANALYSIS ON A DETERMINANT INEQUALITY

本文的目的在于改进已有的两个复矩阵的行列式的上界,以更精细的两个Hermitian正定矩阵和的行列式为基本工具.利用得到的相关一元二次不等式描述的行列式之间的关系,给出了两个复矩阵和的行列式新上界,作为应用可改进华罗庚行列式不等式的上界.

In this ariticle, the main purpose is to improve the upper bound of the determinant of the sum of two complex matrices. By using the implements of the more precise determinant inequality of two Hermitian positive definite matrices, and by the result of the relationship among the determinants described by the quardratic inequality, we obtain a new upper bound of the sum of two complex matrices. As an application of our results, we improve the upper bound of Hua Loo Keng＇s determinant inequality.