On the spectrum in max algebra

0446798 - MÚ 2016 RIV US eng J - Journal Article
Müller, Vladimír - Peperko, A.
On the spectrum in max algebra.
Linear Algebra and Its Applications. Roč. 485, November (2015), s. 250-266. ISSN 0024-3795. E-ISSN 1873-1856
R&D Projects: GA ČR(CZ) GA14-07880S
Institutional support: RVO:67985840
Keywords : non-negativ matrices * max algebra * eigenvalues
Subject RIV: BA - General Mathematics
Impact factor: 0.965, year: 2015
http://www.sciencedirect.com/science/article/pii/S0024379515004139

We give new proofs of several fundamental results of spectral theory in max algebra. This includes the description of the spectrum in max algebra of a given non-negative matrix via local spectral radii, the spectral theorem and the spectral mapping theorem in max algebra. The latter result is also generalized to the setting of power series in max algebra by applying certain continuity properties of the spectrum in max algebra. Our methods enable us to obtain some related results for the usual spectrum of complex matrices and distinguished spectrum for non-negative matrices.
Permanent Link: http://hdl.handle.net/11104/0248758