### Abstract

Means of positive numbers are well-know but the theory of matrix means due to Kubo and Ando is less known. The lecture gives a short introduction to means, the emphasis is on matrices. It is shown that any two-variable-mean of matrices can be extended to more variables. The n-variable-mean M_{n}(A_{1}, A_{2}, …, A_{n}) is defined by a symmetrization procedure when the n-tuple (A_{1}, A_{2}, …, A_{n}) is ordered, it is continuous and monotone in each variable. The geometric mean of matrices has a nice interpretation in terms of an information geometry and the ordering of the n-tuple is not necessary for the definition. It is conjectured that this strong condition might be weakened for some other means, too.

Original language | English |
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Pages (from-to) | 129-139 |

Number of pages | 11 |

Journal | Annales Mathematicae et Informaticae |

Volume | 32 |

Publication status | Published - Jan 1 2005 |

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### Keywords

- Geometric mean
- Information geometry
- Logarithmic mean
- Operator means
- Positive matrices

### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)

### Cite this

*Annales Mathematicae et Informaticae*,

*32*, 129-139.