Orthogonality of matrices

被引：33

作者：

Benitez, Carlos ^{[1
]}

Fernandez, Manuel ^{[1
]}

Soriano, Maria L. ^{[1
]}

机构：

[1] Univ Extremadura, Dept Matemat, E-06071 Badajoz, Spain

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2007年 / 422卷 / 01期

关键词：

orthogonality of matrices; characterization of inner product spaces;

D O I：

10.1016/j.laa.2006.09.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a real finite-dimensional normed space with unit sphere S-X and let LP(X) be the space of linear operators front X into itself. It is proved that X is an inner product space if and only if for A, C epsilon L(X) A perpendicular to C double left right arrow* there exists u is an element of S-X : parallel to A parallel to = parallel to Au parallel to, Au perpendicular to Cu, where perpendicular to denotes Birkhoff orthogonality. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：155 / 163

页数：9

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