# primitive matrix

A nonnegative square matrix^{} $A=({a}_{ij})$ is said to be a if there exists $k$ such that ${A}^{k}\gg 0$, i.e., if there exists $k$ such that for all $i,j$, the $(i,j)$ entry of ${A}^{k}$ is positive.

A sufficient condition for a matrix to be a primitive matrix is for the matrix to
be a nonnegative, irreducible matrix^{} with a positive element^{} on the main diagonal.

Title | primitive matrix |
---|---|

Canonical name | PrimitiveMatrix |

Date of creation | 2013-03-22 13:18:18 |

Last modified on | 2013-03-22 13:18:18 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 12 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 15A51 |

Classification | msc 15A48 |