On perturbation bounds of eigenvalues in Euclidean Jordan Algebras

被引：0

作者：

Seltzer, Kevin ^{[1
]}

Tao, J. ^{[1
]}

机构：

[1] Loyola Univ Maryland, Dept Math & Stat, Baltimore, MD 21210 USA

来源：

LINEAR & MULTILINEAR ALGEBRA | 2015年 / 63卷 / 07期

关键词：

17C20; 17C55; 15A33; octonions; quaternions; Cauchy interlacing theorem; Euclidean Jordan algebra; MATRICES; THEOREM;

D O I：

10.1080/03081087.2014.939174

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In matrix theory, C.-K. Li and R.-C. Li gave the best bound of the difference between eigenvalues of a real/complex Hermitian matrix and the matrix after removing off-diagonal blocks. In this paper, we extend this result to the setting of simple Euclidean Jordan Algebras.

引用

页码：1379 / 1389

页数：11

共 16 条

[1]

[Anonymous], 1990, Matrix perturbation theory

[2]

[Anonymous], 1994, Analysis on Symmetric Cones

[3]

Bhatia R., 1997, Springer Graduate Texts in Mathematics

[4]

DRAY T., 1998, ADV APPL CLIFFORD AL, V8, P341, DOI DOI 10.1007/BF03043104

[5] The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences [J].

Gowda, M. Seetharama ;

Tao, J. .

LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (01) :65-86

[6] Schur complements, Schur determinantal and Haynsworth inertia formulas in Euclidean Jordan algebras [J].

Gowda, M. Seetharama ;

Sznajder, Roman .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (06) :1553-1559

[7] Some inertia theorems in Euclidean Jordan algebras [J].

Gowda, M. Seetharama ;

Tao, Jiyuan ;

Moldovan, Melania .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (8-9) :1992-2011

[8] Automorphism invariance of P- and GUS-properties of linear transformations on Euclidean Jordan algebras [J].

Gowda, MS ;

Sznajder, R .

MATHEMATICS OF OPERATIONS RESEARCH, 2006, 31 (01) :109-123

[9] A note on eigenvalues of perturbed Hermitian matrices [J].

Li, CK ;

Li, RC .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 395 :183-190

[10] Quadratic residual bounds for the Hermitian eigenvalue problem [J].

Mathias, R .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1998, 19 (02) :541-550

← 1 2 →