Currently displaying 1 – 10 of 10

Showing per page

Order by Relevance | Title | Year of publication

Derivatives of orbital function and an extension of Berezin-Gel’fand’s theorem

Tin-Yau TamWilliam C. Hill — 2016

Special Matrices

A generalization of a result of Berezin and Gel’fand in the context of Eaton triples is given. The generalization and its proof are Lie-theoretic free and requires some basic knowledge of nonsmooth analysis. The result is then applied to determine the distance between a point and a G-orbit or its convex hull.We also discuss the derivatives of some orbital functions.

Geometry and inequalities of geometric mean

Trung Hoa DinhSima AhsaniTin-Yau Tam — 2016

Czechoslovak Mathematical Journal

We study some geometric properties associated with the t -geometric means A t B : = A 1 / 2 ( A - 1 / 2 B A - 1 / 2 ) t A 1 / 2 of two n × n positive definite matrices A and B . Some geodesical convexity results with respect to the Riemannian structure of the n × n positive definite matrices are obtained. Several norm inequalities with geometric mean are obtained. In particular, we generalize a recent result of Audenaert (2015). Numerical counterexamples are given for some inequality questions. A conjecture on the geometric mean inequality regarding m pairs...

Page 1

Download Results (CSV)