# matrix condition number is greater or equal to $1$

###### Theorem 1.

The matrix condition number is greater or equal $\mathrm{1}$.

###### Proof.

Let $A$ be a square matrix^{}. Then by properties of a matrix norm^{},

$$1=||I||=||A{A}^{-1}||\le ||{A}^{-1}||||A||.$$ |

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Title | matrix condition number is greater or equal to $1$ |
---|---|

Canonical name | MatrixConditionNumberIsGreaterOrEqualTo1 |

Date of creation | 2013-03-22 15:28:15 |

Last modified on | 2013-03-22 15:28:15 |

Owner | georgiosl (7242) |

Last modified by | georgiosl (7242) |

Numerical id | 10 |

Author | georgiosl (7242) |

Entry type | Theorem |

Classification | msc 65F35 |

Classification | msc 15A12 |

Related topic | MatrixConditionNumber |