A max version of the generalized spectral radius theorem

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• 作者：Yung-Yih Lur
• 关键词：Max algebra ; Maximum circuit geometric mean ; Generalized spectral radius ; Joint spectral radius
• 刊名：Linear Algebra and its Applications
• 出版年：2006
• 出版时间：1 October 2006
• 年：2006
• 卷：418
• 期：1
• 页码：336-346
• 全文大小：152 K

文摘

Let Ψ be a bounded set of n × n nonnegative matrices in max algebra. In this paper we propose the notions of the max algebra version of the generalized spectral radius μ(Ψ) of Ψ, and the max algebra version of the joint spectral radius η(Ψ) of Ψ. The max algebra version of the generalized spectral radius theorem μ(Ψ) = η(Ψ) is established. We propose the relationship between the generalized spectral radius ρ(Ψ) of Ψ (in the sense of Daubechies and Lagarias) and its max algebra version μ(Ψ). Moreover, a generalization of Elsner and van den Driessche’s lemma is presented as well.