The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences

被引：30

作者：

Gowda, M. Seetharama ^{[1
]}

Tao, J. ^{[2
]}

机构：

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

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

来源：

LINEAR & MULTILINEAR ALGEBRA | 2011年 / 59卷 / 01期

关键词：

Euclidean Jordan algebras; quadratic representations; min-max theorem of Hirzebruch; Cauchy interlacing theorem; Schur's theorem; Hadamard's inequality; Fan's trace inequality; LINEAR TRANSFORMATIONS; P-PROPERTIES; INEQUALITY; CONVEXITY; TRACE;

D O I：

10.1080/03081080903346425

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, based on the min-max theorem of Hirzebruch, we formulate and prove the Cauchy interlacing theorem in simple Euclidean Jordan algebras. As a consequence, we relate the inertias of an element and its principal components and extend some well-known matrix theory theorems and inequalities to the setting of simple Euclidean Jordan algebras.

引用

页码：65 / 86

页数：22