## Lectures on linear sequential machines |

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### Contents

Special Topics in Linear Algebra | 3 |

Basic Notions of Sequential Machine | 31 |

Basic Properties of Linear Sequential | 59 |

Copyright | |

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### Common terms and phrases

A-invariant algorithm required assume Chapter classical canonical form companion matrix computable field Corollary coset cycle structure d(qu Define Definition dimension direct sum elementary divisors equations Example exists exp p(x exponent field F finite field finite LSM finite memory finite sequential machine function given Hence homomorphism implies indecomposable input invariant factors invariant subspaces irreducible polynomial isomorphic Lemma Let F Let Mt Let q lg(x linear parallel decomposition linear transformation linearly realizable mA(x max-per minimal form minimal LSM's minimum polynomial monic monoid mv(x nonsingular matrix nontrivial linear parallel Note null null space one-to-one open problem output parallel state realization pd(q proof of Theorem Proposition prove q e Fn q e Q rational canonical form right congruence relation similar strongly connected submachine Suppose Theorem 5.9 trivial vector space x e F X(qu