有关矩阵广义逆AT,S2的惯性指数及其应用（英文）  

Inertia formulae related to the generalized inverse AT,S2 with applications

作　　者：吴中成 贺宁馨 WU Zhongcheng;HE Ningxin(School of Mathematics,Physics and Statistics,Shanghai University of Engineering Science,Shanghai 201620,China;School of Mathematics Science,Guizhou Normal University,Guiyang 550001,China)

机构地区：[1]上海工程技术大学数理与统计学院,上海201620 [2]贵州师范大学数学科学学院,贵州贵阳550001

出　　处：《浙江大学学报（理学版）》2019年第4期395-398,404,共5页Journal of Zhejiang University（Science Edition）

基　　金：Supported by the National Natural Science Foundation of China(11471211);Science Grant from Guizhou Province LH(2014)7062

摘　　要：建立了某些有关矩阵广义逆AT,S^(2)表达式的惯性指数公式。基于所得惯性指数,作为应用研究了矩阵的正定(半正定)性、负定(半负定)性。给出了一些矩阵分别为正定矩阵、半正定矩阵、负定矩阵、半负定矩阵的充分必要条件。In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse AT,S^(2). Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices. Finally,necessary and sufficient conditions for some matrices to be positive definite, positive semi- definite, negative definite and negative semi-definite are given, respectively.

关 键 词：惯性指数 广义逆 正定(半正定) 负定(半负定) 

分 类 号：O151.21[理学—数学]