# reflexive non-degenerate sesquilinear

A non-degenerate sesquilinear form^{} $b:V\times V\to k$ is *reflexive ^{}* if for all $v,w\in V$, if $b(v,w)=0$ then $b(w,v)=0$. This means

$$v\u27c2w\text{if and only if}w\u27c2v.$$ |

It is rare to define perpendicularity^{} for sesquilinear/bilinear maps which are not reflexive because it would require a version of left and right perpendicular^{}. Thus a reflexive sesquilinear/bilinear map is usually synonymous with the existence of perpendicularity.

Title | reflexive non-degenerate sesquilinear |

Canonical name | ReflexiveNondegenerateSesquilinear |

Date of creation | 2013-03-22 15:51:04 |

Last modified on | 2013-03-22 15:51:04 |

Owner | Algeboy (12884) |

Last modified by | Algeboy (12884) |

Numerical id | 10 |

Author | Algeboy (12884) |

Entry type | Definition |

Classification | msc 15A63 |

Synonym | reflexive non-degenerate bilinear |

Synonym | reflexive sesquilinear |

Synonym | reflexive bilinear |

Related topic | SesquilinearFormsOverGeneralFields |

Defines | Reflexive non-degenerate sesquilinear |

Defines | Reflexive non-degenerate bilinear |

Defines | Reflexive |