广义次正定矩阵  

Generalized Positive Subdefinite Matrices

作　　者：袁晖坪[1] 

机构地区：[1]重庆工商大学理学院,重庆南岸区400067

出　　处：《电子科技大学学报》2007年第S1期328-330,345,共4页Journal of University of Electronic Science and Technology of China

基　　金：重庆市自然科学基金(CSTS 2005 BB 0243);重庆市教委科技项目基金(3-10-71)

摘　　要：提出了广义次正定矩阵的概念,研究了Hadamard积与Kronecker积的基本性质,获得了一些新的结果,将著名的Schur定理、华罗庚定理、Openheim不等式、Ostrowski-Taussy不等式等拓广到了广义次正定矩阵上,并将各类实次正定矩阵达到统一.Real metapositive defmite matrix is an important popular subject in matrix theory.The concept of generalized positive subdefinite(GPS)matrix is proposed in this paper.The basic properties,Hadamard product, and Kronecker product GPS matrix are discussed.As applications,some famous theorems and inequalities such as Schur,Hua Luogeng,Openheim,and Ostrowski-Taussy are extended into GPS matrix forms.In addition,some other positive sub-definite matrices are also considered.

关 键 词：准次正定矩阵 广义次正定矩阵 亚正定矩阵 次亚正定矩阵 对称正定矩阵 

分 类 号：O151.21[理学—数学]