On the max version of the generalized spectral radius theorem

Abstract

Let Ψ be a bounded set of n × n non-negative matrices. Recently, the max algebra version μ ( Ψ ) of the generalized spectral radius of Ψ was introduced. We show that μ ( Ψ ) = lim t → ∞ i ( t ) ) 1 / t , where ρ denotes the generalized spectral radius and Ψ ( t ) the Hadamard power of Ψ . This provides a description of μ ( Ψ ) that uses no max terminology. As an application we give a short proof of the max version of the generalized spectral radius theorem.