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

被引：27
|
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.
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页码：65 / 86
页数：22
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