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

Jungers, Raphaël;Protasov, Vladimir;Blondel, Vincent
(2008) Linear Algebra and Its Applications — Vol. 428, n° 10, p. 2296-2311 (2008)

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Abstract
For a given finite set Sigma of matrices with nonnegative integer entries we study the growth with t of max {parallel to A(1)... A(t)parallel to : A(i) epsilon Sigma}. We show how to determine in polynomial time whether this growth is bounded, polynomial, or exponential, and we characterize all possible behaviors. (c) 2007 Elsevier Inc. All rights reserved.
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Jungers, R., Protasov, V., & Blondel, V. (2008). Efficient algorithms for deciding the type of growth of products of integer matrices. Linear Algebra and Its Applications, 428(10), 2296-2311. https://doi.org/10.1016/j.laa.2007.08.001 (Original work published 2008)