In this paper, the contragredient equivalence is extended to several matric
es and a reduced form of the cyclically multiplicable n-tuples of matrices
under this equivalence is defined and constructed. An invariant set of elem
entary divisors (the spectrum of divisors) is found. This set describes com
pletely the reduced form of a given cyclically multiplicable n-tuple. (C) 1
999 Elsevier Science Inc. All rights reserved.