# Löwner’s theorem

A real function $f$ on an interval $I$ is matrix monotone if and only if it is real analytic and has (complex) analytic continuations to the upper and lower half planes such that $\mathrm{\Im}(f)>0$ in the upper half plane.

(Löwner 1934)

Title | Löwner’s theorem |
---|---|

Canonical name | LownersTheorem |

Date of creation | 2013-03-22 13:34:49 |

Last modified on | 2013-03-22 13:34:49 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 7 |

Author | mathcam (2727) |

Entry type | Theorem |

Classification | msc 40A30 |