NUMERICAL RANGE AND POSITIVE BLOCK MATRICES

被引：3

作者：

Bourin, Jean-Christophe ^{[1
]}

Lee, Eun-Young ^{[2
]}

机构：

[1] Univ Bourgogne Franche Comte, CNRS, Lab Math Besancon, UMR 6623, Besancon, France

[2] Kyungpook Natl Univ, KNU Ctr Nonlinear Dynam, Dept Math, Daegu 702701, South Korea

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2021年 / 103卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

numerical range; partitioned matrices; norm inequalities; INEQUALITIES; RADIUS; NORM;

D O I：

10.1017/S0004972720000520

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range W(X) of the off-diagonal block X, especially the distance d from 0 to W(X). A special consequence is an estimate, diamW([(A)(X*) (X)(B)]) - diamW(A + B/2) >= 2d, between the diameters of the numerical ranges for the full matrix and its partial trace.

引用

页码：69 / 77

页数：9

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