Generalized spectral radius and its max algebra version

0395493 - MÚ 2014 RIV US eng J - Článek v odborném periodiku
Müller, Vladimír - Peperko, A.
Generalized spectral radius and its max algebra version.
Linear Algebra and Its Applications. Roč. 439, č. 4 (2013), s. 1006-1016. ISSN 0024-3795. E-ISSN 1873-1856
Grant CEP: GA ČR GA201/09/0473; GA AV ČR IAA100190903
Institucionální podpora: RVO:67985840
Klíčová slova: generalized spectral radius * joint spectral radius * Berger-Wang formula
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.983, rok: 2013
http://www.sciencedirect.com/science/article/pii/S0024379512007380

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).
Trvalý link: http://hdl.handle.net/11104/0223520