Properties of symmetric matrices
type: Item
instance of: scholarly article
title: Properties of symmetric matrices
zbMATH Open document ID: 1087.46011
author: Jaesung Lee
author: Kyung Soo Rim
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-21T00:00:00Z
review text: The two main results in this paper describe the set of extreme and smooth points of the unit ball of the Banach space of real symmetric \( n \times n \)-matrices, where the norm of a matrix is defined as the maximum absolute value of its eigenvalues. It is proved that a symmetric real matrix is an extreme point of the unit ball if and only if all its eigenvalues are \(\pm{1}\). The smooth points of the unit ball are those elements that have exactly one eigenvalue which is \(\pm{1}\).
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 2159785
zbMATH Keywords: extreme point
zbMATH Keywords: smooth point
zbMATH Keywords: unit ball
zbMATH Keywords: Banach space of real symmetric \( n \times n \)-matrices
reviewed by: Juan Francisco Mena Jurado
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.11.011
OpenAlex ID: W2011058266
cites work: Supremum norms for quadratic polynomials
cites work: Q3688914
cites work: Extreme polynomials and multilinear forms on \(\ell_1\)
cites work: The unit ball of \({\mathcal P}(^2\ell_2^2)\)
cites work: Extreme elements of the unit ball of bilinear operators on \(\ell ^ 2_ 2\)
cites work: Extremal structure of the unit ball of \(L^ p(\mu,X)\)
DOI: 10.1016/J.JMAA.2004.11.011
description: scientific article; zbMATH DE number 2159785