About: Generalized spectral radius and its max algebra version

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Let Sigma subset of C-nxn and Psi subset of R-+(nxn) likra be bounded subsets and let rho(Sigma) and mu(Psi) denote the generalized spectral radius of Sigma and the max algebra version of the generalized spectral radius of Psi, respectively. We apply a single matrix description of mu(Psi) to give a new elementary and straightforward proof of the Berger-Wang formula in max algebra and consequently a new short proof of the original Berger-Wang formula in the case of bounded subsets of n x n non-negative matrices. We also obtain a new description of mu(Psi) in terms of the Schur-Hadamard product and prove new trace and max-trace descriptions of mu(Psi) and rho(Sigma). Let Sigma subset of C-nxn and Psi subset of R-+(nxn) likra be bounded subsets and let rho(Sigma) and mu(Psi) denote the generalized spectral radius of Sigma and the max algebra version of the generalized spectral radius of Psi, respectively. We apply a single matrix description of mu(Psi) to give a new elementary and straightforward proof of the Berger-Wang formula in max algebra and consequently a new short proof of the original Berger-Wang formula in the case of bounded subsets of n x n non-negative matrices. We also obtain a new description of mu(Psi) in terms of the Schur-Hadamard product and prove new trace and max-trace descriptions of mu(Psi) and rho(Sigma). (en)
Title	Generalized spectral radius and its max algebra version Generalized spectral radius and its max algebra version (en)
skos:prefLabel	Generalized spectral radius and its max algebra version Generalized spectral radius and its max algebra version (en)
skos:notation	RIV/67985840:_____/13:00395493!RIV14-GA0-67985840
http://linked.open...avai/predkladatel	Matematický ústav AV ČR, v. v. i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/09/0473), P(IAA100190903)
http://linked.open...iv/cisloPeriodika	4
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Müller, Vladimír
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	76320
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/13:00395493
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	generalized spectral radius; joint spectral radius; Berger-Wang formula (en)
http://linked.open.../riv/klicoveSlovo	Berger-Wang formula generalized spectral radius joint spectral radius
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[0879D7A815A6]
http://linked.open...i/riv/nazevZdroje	Linear Algebra and Its Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Methods of function theory and Banach algebras in operator theory IV Orbits, invariant subspaces and positivity in operator theory
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	439
http://linked.open...iv/tvurceVysledku	Müller, Vladimír Peperko, A.
http://linked.open...ain/vavai/riv/wos	000321084700017
issn	0024-3795
number of pages	11 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.laa.2012.09.024

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