广义次正定矩阵的行列式不等式

Determinantal inequality of generalized positive subdefinite matrices

给出了广义次正定矩阵的概念,通过研究它的基本性质及行列式理论,取得一系列新结果,将著名的Schur定理、华罗庚定理、Minkowski不等式、Hadamard不等式、Openheim不等式和Ostrowski Taussy不等式拓广到了广义次正定阵上,扩大了Minkowski不等式的指数范围.

The concept of generalized positive subdefinite matrix is given, and its properties and determinant theories are discussed, and many new results are obtained. As application, some famous theorems and inequalities named after Schur, HUA Loo-geng, Minkowski,Hadamard, Openheim and Ostrowski-Taussy are generalized, and the index scope of Minkowski inequality is enlarged.