Positive matrices partitioned into a small number of Hermitian blocks

被引：12

作者：

Bourin, Jean-Christophe ^{[1
]}

Lee, Eun-Young ^{[2
]}

Lin, Minghua ^{[3
]}

机构：

[1] Univ Franche Comte, Math Lab, F-25000 Besancon, France

[2] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea

[3] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 438卷 / 05期

基金：

新加坡国家研究基金会;

关键词：

Matrix inequalities; Partial trace; Positive definite matrices; Norm; Quaternions;

D O I：

10.1016/j.laa.2012.10.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks: the full matrix is a kind of average of copies of the sum of the diagonal blocks. This entails several eigenvalue inequalities. The proofs use a decomposition lemma for positive matrices, isometries with complex entries, and the Pauli matrices. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：2591 / 2598

页数：8

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