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Efficient algorithms for deciding the type of growth of products of integer matrices

Raphaël Jungers·Vladimir Protasov·Vincent D. Blondel
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Abstract

For a given finite set $Σ$ of matrices with nonnegative integer entries we study the growth of $$ \max_t(Σ) = \max\{\|A_{1}... A_{t}\|: A_i \in Σ\}.$$ We show how to determine in polynomial time whether the growth with $t$ is bounded, polynomial, or exponential, and we characterize precisely all possible behaviors.

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Raphaël Jungers, Vladimir Protasov, Vincent D. Blondel. 2006-04-11. Efficient algorithms for deciding the type of growth of products of integer matrices. https://arxiv.org/abs/cs/0604047

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