The Karcher mean of linearly independent triples

Eduardo Ghiglioni; Yongdo Lim; Miklós Pálfia

doi:10.1016/j.laa.2020.09.041

The Karcher mean of linearly independent triples

Eduardo Ghiglioni
, Yongdo Lim
, Miklós Pálfia

Department of Mathematics

Sungkyunkwan University
Universidad Nacional de La Plata
University of Szeged

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We present a classification of 2×2 positive definite Hermitian triples of determinant one having the Karcher mean formula [Formula presented]. We further show that it is equivalent to the trace condition: tr(AB⁻¹)=tr(AC⁻¹)=tr(BC⁻¹) for linearly independent triples.

Original language	English
Pages (from-to)	203-221
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	610
DOIs	https://doi.org/10.1016/j.laa.2020.09.041
State	Published - 1 Feb 2021

Keywords

Karcher mean
Pauli matrix
Positive definite matrix

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10.1016/j.laa.2020.09.041

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title = "The Karcher mean of linearly independent triples",

abstract = "We present a classification of 2×2 positive definite Hermitian triples of determinant one having the Karcher mean formula [Formula presented]. We further show that it is equivalent to the trace condition: tr(AB−1)=tr(AC−1)=tr(BC−1) for linearly independent triples.",

keywords = "Karcher mean, Pauli matrix, Positive definite matrix",

author = "Eduardo Ghiglioni and Yongdo Lim and Mikl{\'o}s P{\'a}lfia",

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year = "2021",

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doi = "10.1016/j.laa.2020.09.041",

language = "English",

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T1 - The Karcher mean of linearly independent triples

AU - Ghiglioni, Eduardo

AU - Lim, Yongdo

AU - Pálfia, Miklós

PY - 2021/2/1

Y1 - 2021/2/1

N2 - We present a classification of 2×2 positive definite Hermitian triples of determinant one having the Karcher mean formula [Formula presented]. We further show that it is equivalent to the trace condition: tr(AB−1)=tr(AC−1)=tr(BC−1) for linearly independent triples.

AB - We present a classification of 2×2 positive definite Hermitian triples of determinant one having the Karcher mean formula [Formula presented]. We further show that it is equivalent to the trace condition: tr(AB−1)=tr(AC−1)=tr(BC−1) for linearly independent triples.

KW - Karcher mean

KW - Pauli matrix

KW - Positive definite matrix

UR - https://www.scopus.com/pages/publications/85092185583

U2 - 10.1016/j.laa.2020.09.041

DO - 10.1016/j.laa.2020.09.041

M3 - Article

AN - SCOPUS:85092185583

SN - 0024-3795

VL - 610

SP - 203

EP - 221

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The Karcher mean of linearly independent triples

Abstract

Keywords

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