Inequalities for the Wasserstein mean of positive definite matrices

Rajendra Bhatia; Tanvi Jain; Yongdo Lim

doi:10.1016/j.laa.2018.03.017

Inequalities for the Wasserstein mean of positive definite matrices

Rajendra Bhatia
, Tanvi Jain
, Yongdo Lim

Department of Mathematics

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

29 Scopus citations

Abstract

We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

Original language	English
Pages (from-to)	108-123
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	576
DOIs	https://doi.org/10.1016/j.laa.2018.03.017
State	Published - 1 Sep 2019

Keywords

Cartan mean
Log Euclidean mean
Majorisation
Positive definite matrices
Unitarily invariant norm
Wasserstein mean

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10.1016/j.laa.2018.03.017

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title = "Inequalities for the Wasserstein mean of positive definite matrices",

abstract = "We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.",

keywords = "Cartan mean, Log Euclidean mean, Majorisation, Positive definite matrices, Unitarily invariant norm, Wasserstein mean",

author = "Rajendra Bhatia and Tanvi Jain and Yongdo Lim",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

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day = "1",

doi = "10.1016/j.laa.2018.03.017",

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T1 - Inequalities for the Wasserstein mean of positive definite matrices

AU - Bhatia, Rajendra

AU - Jain, Tanvi

AU - Lim, Yongdo

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

AB - We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

KW - Cartan mean

KW - Log Euclidean mean

KW - Majorisation

KW - Positive definite matrices

KW - Unitarily invariant norm

KW - Wasserstein mean

UR - https://www.scopus.com/pages/publications/85044325827

U2 - 10.1016/j.laa.2018.03.017

DO - 10.1016/j.laa.2018.03.017

M3 - Article

AN - SCOPUS:85044325827

SN - 0024-3795

VL - 576

SP - 108

EP - 123

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Inequalities for the Wasserstein mean of positive definite matrices

Abstract

Keywords

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