# cyclic vector theorem

Let $K$ be a field, $V$ a $K$-vector space^{} of dimension^{} $n$,
and $f:V\u27f6V$ a linear transformation. Then $f$
has a cyclic vector if and only if every linear transformation $g:V\u27f6V$ which commutes with $f$ is a polynomial^{} of $K[X]$ evaluated in $f$.

Title | cyclic vector theorem |
---|---|

Canonical name | CyclicVectorTheorem |

Date of creation | 2013-03-22 14:14:16 |

Last modified on | 2013-03-22 14:14:16 |

Owner | gumau (3545) |

Last modified by | gumau (3545) |

Numerical id | 5 |

Author | gumau (3545) |

Entry type | Theorem |

Classification | msc 15A04 |

Related topic | CyclicSubspace |