A Geometric Mean for Symmetric Spaces of Noncompact Type

被引：0

作者：

Liao, Ming ^{[1
]}

Liu, Xuhua ^{[2
]}

Tam, Tin-Yau ^{[1
]}

机构：

[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[2] Univ Tennessee, Dept Math, Chattanooga, TN 37403 USA

来源：

JOURNAL OF LIE THEORY | 2014年 / 24卷 / 03期

关键词：

Geometric mean; positive definite matrices; symmetric spaces; semisimple Lie groups; geodesics; log majorization; Kostant's order; INEQUALITY; MATRICES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The concept of the t-geometric mean of two positive definite matrices is extended to symmetric spaces of noncompact type. The t-geometric mean of two points in such a symmetric space yields the unique geodesic joining the points and the geometric mean is the midpoint. A parametrization of the geodesic in terms of the two points is given. Inequalities about geometric mean and geodesic triangle are given in terms of Kostant's pre-order on semisimple Lie groups as well as on their Lie algebras.

引用

页码：725 / 736

页数：12

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