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ON THE CONTINUITY OF THE GENERALIZED SPECTRAL RADIUS IN MAX ALGEBRA

By Aljosa Peperko

Abstract

Given a bounded set Ψ of n × n non-negative matrices, let ρ(Ψ) and µ(Ψ) denote the generalized spectral radius of Ψ and its max version, respectively. We show that µ(Ψ) =) 1/t sup t∈(0,∞) n −1 ρ(Ψ (t) ), where Ψ (t) denotes the Hadamard power of Ψ. We apply this result to give a new short proof of a known fact that µ(Ψ) is continuous on the Hausdorff metric space (β, H) of all nonempty compact collections of n × n non-negative matrices

Topics: Key words, Maximum circuit geometric mean, Max algebra, Non-negative matrices, Generalized spectral radius, Joint spectral radius, Continuity, Hausdorff metric, Hadamard powers, Schur powers
Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.417.7374
Provided by: CiteSeerX
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