Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897940 | Linear Algebra and its Applications | 2018 | 17 Pages |
Abstract
We introduce a class of repetition invariant geometric means and obtain corresponding contractive barycentric maps of integrable Borel probability measures on the Cartan-Hadamard Riemannian manifold of positive definite matrices. They retain most of the properties of the Cartan barycenter and lead to the conclusion that there are infinitely many distinct contractive barycentric maps. Inequalities from the derived geometric means including the Yamazaki inequality and unitarily invariant norm inequalities are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sejong Kim, Hosoo Lee, Yongdo Lim,