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Start Over Subject Matematika Date Unknown

21. Geometry and inequalities of geometric mean

Creator:
Dinh, Trung Hoa, Ahsani, Sima, and Tam, Tin-Yau
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
Matematika, matematika, mathematics, geometric mean, positive definite matrix, log majorization, geodesics, geodesically convex, geodesic convex hull, unitarily invariant norm, 13, and 51
Language:
English
Description:
We study some geometric properties associated with the t-geometric means A ♯_{t} B:= A^{1/2}(A^{-1/2}BA^{-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 of positive definite matrices is posted., Trung Hoa Dinh, Sima Ahsani, Tin-Yau Tam., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public