# matrix norm

A is a norm on the set ${M}_{m\times n}(R)$ of $m\times n$ matrices over a ring $R$, and is usually denoted by $||\cdot ||$.

The Frobenius matrix norm $||\cdot |{|}_{F}$ and the matrix $p$-norm (http://planetmath.org/MatrixPNorm) $||\cdot |{|}_{p}$
are the most frequently used matrix norms^{}.

A vector norm is a matrix norm for which the ring $R$ is a field.

Title | matrix norm |
---|---|

Canonical name | MatrixNorm |

Date of creation | 2013-03-22 11:43:20 |

Last modified on | 2013-03-22 11:43:20 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 17 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 65F35 |

Classification | msc 43-02 |

Classification | msc 00A69 |

Related topic | VectorNorm |

Related topic | FrobeniusMatrixNorm |

Related topic | MatrixPnorm |