Some inertia theorems in Euclidean Jordan algebras

被引：30

作者：

Gowda, M. Seetharama ^{[1
]}

Tao, Jiyuan ^{[2
]}

Moldovan, Melania ^{[1
]}

机构：

[1] Univ Maryland, Dept Math & Stat, Baltimore, MD 21250 USA

[2] Loyola Coll, Dept Math Sci, Baltimore, MD 21210 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 8-9期

关键词：

Euclidean Jordan algebra; Inertia; Sylvester's law of inertia; Lyapunov transformation; Quadratic representation; Cone spectrum; Ostrowski-Schneider inertia theorem; LINEAR TRANSFORMATIONS; SYLVESTERS LAW; P-PROPERTIES; CONES;

D O I：

10.1016/j.laa.2008.11.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with some inertia theorems in Euclidean Jordan algebras. First, based on the continuity of eigenvalues, we give an alternate proof of Kaneyuki's generalization of Sylvester's law of inertia in simple Euclidean Jordan algebras. As a consequence, we show that the cone spectrum of any quadratic representation with respect to a symmetric cone is finite. Second, we present Ostrowski-Schneider type inertia results in Euclidean Jordan algebras. In particular, we relate the inertias of objects a and x in a Euclidean Jordan algebra when L-a(x) > 0 or S-a(x) > 0, where L-a and S-a denote Lyapunov and Stein transformations, respectively. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1992 / 2011

页数：20

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