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

Raphaël Jungers, Vladimir Protasov, Vincent D. Blondel

For a given finite set $\Sigma$ of matrices with nonnegative integer entries we study the growth of $$\underset{t}{\max }(\Sigma )=\max \{\Vert A_1...A_t\Vert :A_i\in \Sigma \}.$$ We show how to determine in p…