A differential geometric approach to the geometric mean of symmetric positive-definite matrices

被引：501

作者：

Moakher, M ^{[1
]}

机构：

[1] Tunis El Manar Univ, Natl Engn Sch Tunis, Lab Math & Numer Modeling Engn Sci, ENIT,LAMSIN, Tunis 1002, Tunisia

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2005年 / 26卷 / 03期

关键词：

geometric mean; positive-definite symmetric matrices; Riemannian distance; geodesics;

D O I：

10.1137/S0895479803436937

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce metric-based means for the space of positive-definite matrices. The mean associated with the Euclidean metric of the ambient space is the usual arithmetic mean. The mean associated with the Riemannian metric corresponds to the geometric mean. We discuss some invariance properties of the Riemannian mean and we use differential geometric tools to give a characterization of this mean.

引用

页码：735 / 747

页数：13

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