Title: Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras
Authors: Baes, Michel # ×
Issue Date: Apr-2007
Publisher: Elsevier science inc
Series Title: Linear algebra and its applications vol:422 issue:2-3 pages:664-700
Abstract: We study in this paper several properties of the eigenvalues function of a Euclidean Jordan algebra, extending several known results in the frarnework of symmetric matrices. In particular, we give a concise form for the directional differential of a single eigenvalue. We especially focus on spectral functions F on Euclidean Jordan algebras, which are the composition of a symmetric real-valued function f with the eigenvalues function. We explore several properties off that are transferred to F, in particular convexity, strong convexity and differentiability. Spectral mappings are also considered, a special case of which is the gradient mapping of a spectral function. Answering a problem proposed by H. Sendov, we give a formula for the Jacobian of these functions. (c) 2006 Elsevier Inc. All rights reserved.
ISSN: 0024-3795
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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