# diagonally dominant matrix

Let $A$ be a square matrix^{} of order $n$ with entries ${a}_{ij}$
which are real or complex.
Then $A$ is said to be *diagonally dominant* if

$$|{a}_{ii}|\ge \sum _{j=1,j\ne i}^{n}|{a}_{ij}|$$ |

for $i$ from $1$ to $n$.

In addition $A$ is said to be *strictly diagonally dominant* if

$$|{a}_{ii}|>\sum _{j=1,j\ne i}^{n}|{a}_{ij}|$$ |

for $i$ from $1$ to $n$.

Title | diagonally dominant matrix |
---|---|

Canonical name | DiagonallyDominantMatrix |

Date of creation | 2013-03-22 13:47:46 |

Last modified on | 2013-03-22 13:47:46 |

Owner | Daume (40) |

Last modified by | Daume (40) |

Numerical id | 7 |

Author | Daume (40) |

Entry type | Definition |

Classification | msc 15-00 |

Synonym | diagonally dominant |

Synonym | strictly diagonally dominant |

Defines | strictly diagonally dominant matrix |