Repetition invariant geometric means

Repetition invariant geometric means

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 t...

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Veröffentlicht in:Linear algebra and its applications 2018-05, Vol.544, p.443-459
Hauptverfasser: Kim, Sejong, Lee, Hosoo, Lim, Yongdo
Format: Artikel
Sprache:eng
Schlagworte:
Borel probability measure
Center of gravity
Contractive barycentric map
Geometric mean
Geometry
Inequalities
Invariants
Linear algebra
Mathematical analysis
Matrix
Matrix methods
Positive definite matrix
Probability
Repetition
Repetition invariancy
Riemann manifold
Yamazaki inequality
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Zusammenfassung: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2018.01.024