准正定矩阵的行列式不等式  

DETERMINANTAL INEQUALITY OF ALMOST POSITIVE DEFINITE MATRICES

作　　者：袁晖坪[1] 郭伟[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《数学杂志》2008年第5期514-518,共5页Journal of Mathematics

基　　金：重庆市自然科学基金资助(CSTS2005BB0243);重庆市教委科技项目基金资助(KJ0707023)

摘　　要：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.

关 键 词：准正定矩阵 亚正定矩阵 次正定矩阵 行列式 不等式 

分 类 号：O151.21[理学—数学]