准正定矩阵  

Almost positive definite matrices

作　　者：袁晖坪[1] 王文惠[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《辽宁工程技术大学学报（自然科学版）》2009年第1期155-157,共3页Journal of Liaoning Technical University (Natural Science)

基　　金：重庆市科技攻关基金资助项目(CSTC2006EA0005);重庆市教委科技基金资助项目(KJ0707023)

摘　　要：为了统一研究各类正定矩阵与次正定矩阵,提出了准正定矩阵的概念,研究了它及其Hadamard积与Kronecker积的基本性质,获得了许多新的结果,改进并推广了实对称阵的Schur定理、华罗庚定理及Minkowski、Ky Fan等著名不等式,扩大了Minkowski不等式的指数范围,并将各类正定矩阵与次正定矩阵统一起来。For unifying the research into a variety of positive definite matrices and positive sub-definite matrices, the concept of almost positive definite matrix is given. The basic properties of it and its Hadamard product and Kronecker product are discussed, and many new results are obtained. As applications, some famous theorem and inequalities named after Schur, Hua Luogeng, Hadamard, Oppenheim, Ostrowski-Taussky, Minkowski, Ky Fan, are generalized and improved, and the index scope of Minkowski inequality is enlarged. A variety of positive definite matrix and positive sub-definite matrix are unified.

关 键 词：准正定矩阵 HADAMARD积 KRONECKER积 不等式 

分 类 号：O151.21[理学—数学]