Analyticity of the Karcher mean coefficient maps

Jimmie Lawson; Yongdo Lim

doi:10.1016/j.laa.2021.06.009

Analyticity of the Karcher mean coefficient maps

Jimmie Lawson, Yongdo Lim

Department of Mathematics

Louisiana State University

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

5 Scopus citations

Abstract

The main concern of this paper is the three-variable Karcher (alternatively, Riemannian or Cartan) matrix mean for 2×2 linearly independent triples of positive definite matrices. We show that such triples form an analytic manifold and obtain three analytic functions from (1,∞)²×(0,π/2) to (0,1) realizing the Karcher mean as a linear combination of variables.

Original language	English
Pages (from-to)	162-184
Number of pages	23
Journal	Linear Algebra and Its Applications
Volume	627
DOIs	https://doi.org/10.1016/j.laa.2021.06.009
State	Published - 15 Oct 2021

Keywords

Karcher mean
Moore-Penrose inverse
Positive definite matrix
Real analytic

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10.1016/j.laa.2021.06.009

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abstract = "The main concern of this paper is the three-variable Karcher (alternatively, Riemannian or Cartan) matrix mean for 2×2 linearly independent triples of positive definite matrices. We show that such triples form an analytic manifold and obtain three analytic functions from (1,∞)2×(0,π/2) to (0,1) realizing the Karcher mean as a linear combination of variables.",

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AU - Lim, Yongdo

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AB - The main concern of this paper is the three-variable Karcher (alternatively, Riemannian or Cartan) matrix mean for 2×2 linearly independent triples of positive definite matrices. We show that such triples form an analytic manifold and obtain three analytic functions from (1,∞)2×(0,π/2) to (0,1) realizing the Karcher mean as a linear combination of variables.

KW - Karcher mean

KW - Moore-Penrose inverse

KW - Positive definite matrix

KW - Real analytic

UR - https://www.scopus.com/pages/publications/85108360681

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DO - 10.1016/j.laa.2021.06.009

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VL - 627

SP - 162

EP - 184

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Analyticity of the Karcher mean coefficient maps

Abstract

Keywords

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