Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/68673
Type: Artigo de periódico
Title: On the geometrical structure of symmetric matrices
Author: Andreani, R
Raydan, M
Tarazaga, P
Abstract: The identity ray, alpha I for alpha > 0, can be seen as the center ray of the cone of symmetric and positive definite (SPD) matrices. In that sense, the angle that any SPD matrix forms with the identity plays a very important role to understand the geometrical structure of the cone. In this work, we extend this relationship, and analyze the geometrical structure of symmetric matrices including the location of all orthogonal matrices, not only the identity matrix. This geometrical understanding leads to new results in the subspace of symmetric matrices. We also extend some of the geometrical results for the case of general (not necessarily symmetric) nonsingular matrices. (C) 2012 Elsevier Inc. All rights reserved.
Subject: Cones of matrices
Orthogonality
Frobenius norm
Country: EUA
Editor: Elsevier Science Inc
Rights: fechado
Identifier DOI: 10.1016/j.laa.2012.07.048
Date Issue: 2013
Appears in Collections:Unicamp - Artigos e Outros Documentos

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