# hyperplane

Let $E$ be a linear space^{} over a field $k$. A hyperplane^{} $H$ in $E$ is defined as the set of the form

$$H=\{x\in E:f(x)=a\}$$ |

where $a\in k$ and $f$ is a nonzero linear functional^{}, $f:E\to k$. If $k=\mathbb{R}$ or $\u2102$, then $H$ is called a *real hyperplane* or *complex hyperplane* respectively.

Remark. When $k=\u2102$, the word “hyperplane” also has a more restrictive meaning: it is the zero set of a complex linear functional (by setting $a=0$ above).

Title | hyperplane |
---|---|

Canonical name | Hyperplane |

Date of creation | 2013-03-22 15:15:12 |

Last modified on | 2013-03-22 15:15:12 |

Owner | georgiosl (7242) |

Last modified by | georgiosl (7242) |

Numerical id | 9 |

Author | georgiosl (7242) |

Entry type | Definition |

Classification | msc 46H05 |

Defines | real hyperplane |

Defines | complex hyperplane |