# necessary and sufficient condition for diagonalizability

Let $k$ be a field, $V$ a vector space^{} over $k$ of dimension^{} $n$,
and $T\in \mathrm{End}(V)$. Then $T$ is diagonalizable^{} if and only if its minimal polynomial^{} (http://planetmath.org/MinimalPolynomialEndomorphism) has no multiple roots^{} and all its roots lie in $k$.

Title | necessary and sufficient condition for diagonalizability |
---|---|

Canonical name | NecessaryAndSufficientConditionForDiagonalizability |

Date of creation | 2013-03-22 14:15:41 |

Last modified on | 2013-03-22 14:15:41 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 11 |

Author | Mathprof (13753) |

Entry type | Theorem |

Classification | msc 15A04 |