# positive definite form

A bilinear form^{} $B$ on a real or complex vector space $V$ is positive definite^{} if $B(x,x)>0$ for all nonzero vectors $x\in V$. On the other hand, if $$ for all nonzero vectors $x\in V$, then we say $B$ is negative definite. If $B(x,x)\ge 0$ for all vectors $x\in V$, then we say
$B$ is nonnegative definite. Likewise,
if $B(x,x)\le 0$ for all vectors $x\in V$, then we say
$B$ is nonpositive definite.

A form which is neither positive definite nor negative definite is called indefinite.

Title | positive definite form |

Canonical name | PositiveDefiniteForm |

Date of creation | 2013-03-22 12:25:50 |

Last modified on | 2013-03-22 12:25:50 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 5 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 11E39 |

Classification | msc 15A63 |

Classification | msc 47A07 |

Synonym | positive definite |

Synonym | negative definite form |

Synonym | negative definite |

Synonym | indefinite form |

Synonym | indefinite |

Synonym | nonnegative definite |

Synonym | nonpositive definite |