On cone of nonsymmetric positive semidefinite matrices

被引：6

作者：

Wang, Yingnan ^{[1
]}

Xiu, Naihua ^{[1
]}

Han, Jiye ^{[2
]}

机构：

[1] Beijing Jiaotong Univ, Dept Appl Math, Beijing 100044, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 433卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Nonsymmetric positive semidefinite matrix; Hyperbolic cone; Facial structure; Maximal convex subcone; P-0-matrix; Projection; HOMOGENEOUS CONVEX CONES; HYPERBOLIC POLYNOMIALS;

D O I：

10.1016/j.laa.2010.03.042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we analyze and characterize the cone of nonsymmetric positive semidefinite matrices (NS-psd). Firstly, we study basic properties of the geometry of the NS-psd cone and show that it is a hyperbolic but not homogeneous cone. Secondly, we prove that the NS-psd cone is a maximal convex subcone of P-0-matrix cone which is not convex. But the interior of the NS-psd cone is not a maximal convex subcone of P-matrix cone. As the byproducts, some new sufficient and necessary conditions for a nonsymmetric matrix to be positive semidefinite are given. Finally, we present some properties of metric projection onto the NS-psd cone. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：718 / 736

页数：19

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