# anti-idempotent

An element $x$ of a ring is called an anti-idempotent element, or simply an anti-idempotent if ${x}^{2}=-x$.

The term is most often used in linear algebra^{}. Every anti-idempotent matrix over a field is diagonalizable. Two anti-idempotent matrices are similar if and only if they have the same rank.

Title | anti-idempotent |
---|---|

Canonical name | Antiidempotent |

Date of creation | 2013-03-22 13:47:22 |

Last modified on | 2013-03-22 13:47:22 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 4 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 16U99 |

Related topic | LinearInvolution |