准正定矩阵的行列式不等式

DETERMINANTAL INEQUALITY OF ALMOST POSITIVE DEFINITE MATRICES

本文研究了各类正定矩阵与次正定矩阵的基本性质及行列式理论,提出了准正定矩阵的概念,获得了许多新的结果,推广了Hadamard、Openheim、Ostrowski-Taussky与Minkowski等著名不等式以及屠伯埙、杨新民等的有关结果,扩大了Minkowski不等式的指数范围.

The text for making every variety pesitive definite matrix and positive sub-definite matrix to unification, the concept of almost positive definite matrix is given, and its properties and determinant theories are discussed, and many new results are obtained. As applications, some famous inequalities named after Hadamard, Oppenheim, Ostrowski-Taussky, Minkowski, Tu Bo-xun and Yang Xin-min et al are generalized, and the index scope of Minkowski inequality is enlarged.