Abstract
Given a pair of matrices ( A, B ), we can associate to each nice basis of the controllability subspace of ( A, B ) a set of integers to be called the indices of the basis. Each set provides partial information about the similarity class of A . The relationship between several sets of indices as well as the constraints that they impose on the invariant factors of A are investigated. Special attention is paid to the controllability and Hermite indices of a given pair ( A, B ).
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