### Abstract

It is shown that any two-variable-mean of positive matrices (studied by Kubo and Ando) can be extended to more variables. The n- variable-mean M _{n}(A_{1},A_{2},...,A_{n}) la defined by a symmetrizatlon procedure when the n-tuple (A_{1}, A_{2},.,., A_{n}) is ordered, la monotone In each variable, and satisfies the transformer Inequality. Thin approach la motivated by the paper of Ando, Li, and Mathias on geometric means [Linear Algebra Appl., 386 (2004), pp. 305-334]. Special attention is paid to the logarithmic mean. It Is conjectured that for matrix means the symmetrization procedure converges for all triplets.

Original language | English |
---|---|

Pages (from-to) | 712-720 |

Number of pages | 9 |

Journal | SIAM Journal on Matrix Analysis and Applications |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 |

### Fingerprint

### Keywords

- Geometric mean
- Logarithmic mean
- Matrix mean

### ASJC Scopus subject areas

- Algebra and Number Theory
- Applied Mathematics
- Analysis

### Cite this

*SIAM Journal on Matrix Analysis and Applications*,

*27*(3), 712-720. https://doi.org/10.1137/050621906

**Means of positive numbers and matrices.** / Petz, D.; Temesi, Róbert.

Research output: Contribution to journal › Article

*SIAM Journal on Matrix Analysis and Applications*, vol. 27, no. 3, pp. 712-720. https://doi.org/10.1137/050621906

}

TY - JOUR

T1 - Means of positive numbers and matrices

AU - Petz, D.

AU - Temesi, Róbert

PY - 2005

Y1 - 2005

N2 - It is shown that any two-variable-mean of positive matrices (studied by Kubo and Ando) can be extended to more variables. The n- variable-mean M n(A1,A2,...,An) la defined by a symmetrizatlon procedure when the n-tuple (A1, A2,.,., An) is ordered, la monotone In each variable, and satisfies the transformer Inequality. Thin approach la motivated by the paper of Ando, Li, and Mathias on geometric means [Linear Algebra Appl., 386 (2004), pp. 305-334]. Special attention is paid to the logarithmic mean. It Is conjectured that for matrix means the symmetrization procedure converges for all triplets.

AB - It is shown that any two-variable-mean of positive matrices (studied by Kubo and Ando) can be extended to more variables. The n- variable-mean M n(A1,A2,...,An) la defined by a symmetrizatlon procedure when the n-tuple (A1, A2,.,., An) is ordered, la monotone In each variable, and satisfies the transformer Inequality. Thin approach la motivated by the paper of Ando, Li, and Mathias on geometric means [Linear Algebra Appl., 386 (2004), pp. 305-334]. Special attention is paid to the logarithmic mean. It Is conjectured that for matrix means the symmetrization procedure converges for all triplets.

KW - Geometric mean

KW - Logarithmic mean

KW - Matrix mean

UR - http://www.scopus.com/inward/record.url?scp=33746137762&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746137762&partnerID=8YFLogxK

U2 - 10.1137/050621906

DO - 10.1137/050621906

M3 - Article

VL - 27

SP - 712

EP - 720

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 3

ER -