Monotone metrics on matrix spaces

Research output: Contribution to journalArticle

253 Citations (Scopus)

Abstract

The study of monotone inner products under stochastic mappings on the space of matrices was initiated by Morozova and Chentsov, motivated by information geometry. They did not show a monotone metric, but proposed several candidates. The main result of the present paper is to provide an abundance of monotone metrics by means of operator monotone functions and to characterize them. It turns out that there is a correspondence between monotone metrics and operator means in the sense of Kubo and Ando. It follows that all proposals of Morozova and Chentsov are indeed monotone metrics.

Original languageEnglish
Pages (from-to)81-96
Number of pages16
JournalLinear Algebra and Its Applications
Volume244
DOIs
Publication statusPublished - Sep 1 1996

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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