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On the other hand, in case of a finite field generators of polynomial invariants are not known even for a pair of [Formula: see text] matrices. Working over an arbitrary field we classified all [Formula: see text]-orbits on m-tuples of [Formula: see text] nilpotent matrices for all [Formula: see text]. As a consequence, we obtained a minimal separating set for the algebra of [Formula: see text]-invariant polynomial functions of m-tuples of [Formula: see text] nilpotent matrices. 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