# self consistent matrix norm

A matrix norm^{} $N$ is said to be *self consistent* if

$$N(\mathrm{\mathbf{A}\mathbf{B}})\le N(\mathbf{A})\cdot N(\mathbf{B})$$ |

for all pairs of matrices $\mathbf{A}$ and $\mathbf{B}$ such that $\mathrm{\mathbf{A}\mathbf{B}}$ is defined.

Title | self consistent matrix norm |

Canonical name | SelfConsistentMatrixNorm |

Date of creation | 2013-03-22 13:39:22 |

Last modified on | 2013-03-22 13:39:22 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 10 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 15A60 |

Related topic | GelfandSpectralRadiusTheorem |

Defines | self consistent norm |

Defines | self-consistent matrix norm |

Defines | self-consistent norm |

Defines | self-consistent |

Defines | self consistent |