# quadratic function associated with a linear functional

Let $V$ be a real hilbert space^{} (and thus an inner product space^{}), and
let $f$ be a continuous^{} linear functional^{} on $V$. Then $f$ has an associated quadratic function $\phi :V\to \mathbb{R}$
given by

$$\phi (v)=\frac{1}{2}{\parallel v\parallel}^{2}-f(v)$$ |

Title | quadratic function associated with a linear functional |
---|---|

Canonical name | QuadraticFunctionAssociatedWithALinearFunctional |

Date of creation | 2013-03-22 14:00:23 |

Last modified on | 2013-03-22 14:00:23 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 7 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 11Exx |

Classification | msc 46Exx |

Related topic | HilbertSpace |

Related topic | InnerProductSpace |