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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper Title:
A Generalization of a Trace Inequality for Positive Definite Matrices
Author(s):
E. V. Belmega, M. Jungers, and S. Lasaulce
Université Paris-Sud Xi, SUPELEC,
Laboratoire Des Signaux Et Systèmes,
Gif-Sur-Yvette,
France.
belmega@lss.supelec.fr
http://veronica.belmega.lss.supelec.fr
CNRS, ENSEM, CRAN, Vandoeuvre,
France.
marc.jungers@cran.uhp-nancy.fr
http://perso.ensem.inpl-nancy.fr/Marc.Jungers/
CNRS, SUPELEC, Laboratoire des Signaux et
Systèmes,
Gif-Sur-Yvette,
France.
lasaulce@lss.supelec.fr
http://samson.lasaulce.lss.supelec.fr
Abstract:
In this note, we provide a generalization of the trace inequality derived in [Belmega].
More precisely, we prove that for arbitrary K ≥ 1 where Tr(∙) denotes the matrix trace operator, A1, B1 are any positive definite matrices and Ak, Bk for all k∈{2,...,k}, are any positive semidefinite matrices.
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