Means of positive numbers and matrices

D. Petz, Róbert Temesi

Research output: Contribution to journalArticle

34 Citations (Scopus)

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(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.

Original languageEnglish
Pages (from-to)712-720
Number of pages9
JournalSIAM Journal on Matrix Analysis and Applications
Volume27
Issue number3
DOIs
Publication statusPublished - 2005

Fingerprint

Linear algebra
Logarithmic Mean
n-tuple
Positive Matrices
Symmetrization
Geometric mean
Transformer
Monotone
Converge

Keywords

  • Geometric mean
  • Logarithmic mean
  • Matrix mean

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Analysis

Cite this

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

In: SIAM Journal on Matrix Analysis and Applications, Vol. 27, No. 3, 2005, p. 712-720.

Research output: Contribution to journalArticle

Petz, D. ; Temesi, Róbert. / Means of positive numbers and matrices. In: SIAM Journal on Matrix Analysis and Applications. 2005 ; Vol. 27, No. 3. pp. 712-720.
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