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A-invariant algorithm arbitrary field called canonical form canonical realization column reduced form completely observable constant linear system constructed controllability coprime cyclic subspaces DEFINITION denote dim(X dimension direct sum decomposition elements equi equivalence classes equivalent to F,G externally equivalent feedback equivalent field F following theorem H(Is infinite field input input-output map integers internally isomorphic invariant factors irreducible fraction representation Kalman least common denominator least common multiple lemma Let F,G,H linear dynamical system linear operator linear system F,G,H linear system theory matrix Q McMillan degree minimal column list minimal constant linear minimal generating set minimal polynomial minimal realization modulo monic nonsingular matrix polynomial matrix polynomial of F prime system principal ideal domains proper rational matrix Proposition 6.l8 rank Q rational diagonal matrix reachability and observability reachable and completely Remark space description sublemma subset system x theorem 4.8 Theorem 6.l2 transfer equivalent transfer function matrix uniquely determined vector space weak equivalence