Analyticity of the Karcher mean coefficient maps

Analyticity of the Karcher mean coefficient maps

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) real...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Linear algebra and its applications 2021-10, Vol.627, p.162-184
Hauptverfasser: Lawson, Jimmie, Lim, Yongdo
Format: Artikel
Sprache:eng
Schlagworte:
Analytic functions
Karcher mean
Linear algebra
Mathematical analysis
Matrices (mathematics)
Moore-Penrose inverse
Positive definite matrix
Real analytic
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2021.06.009