Abstract
Our main aim is to give a complete characterization of the reducibility sets of continuous 1-parameter families of sequences of matrices, which turn out to be the Fσ -sets. We also show that for any Fσ -set containing zero, one can find a family with this reducibility set. In addition, we obtain corresponding results for the reducibility-stability set and we give an optimal condition for the reducibility to a diagonal matrix in terms of the Lyapunov exponents.
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