A characterization of the joint spectral radius, due to Chen and Zhou, relies on the limit superior of the k-th root of the dominant trace over products of matrices of length k. In this note, a sufficient condition is given such that the limit superior takes the form of a limit. This result is useful while estimating the joint spectral radius. Although it applies to a restricted class of matrices, it appears to be relevant to many realistic situations. http://math.technion.ac.il/iic/ela 1

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... heless, the computation of the joint spectral radius remains a tough challenge since the main difficulty comes from the cardinality of Π k as k grows, or the construction of extremal polytope norms [9] , or the size of the eigenproblem as a result of Kronecker and semidefinite liftings [2] .