The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order

By T. Yamazaki. 2012

52 citations recorded by the source corpus.

The Riemannian mean on the convex cone of positive definite matrices is a kind of geometric mean of n -matrices which is an extension of the geometric mean of two-matrices. In this paper, we derive the Ando-Hiai inequality for the Riemannian mean which is an extension of the well-known Ando-Hiai inequality of two-matrices. Moreover, we shall show an extension of a characterization of chaotic order. Lastly, we will give a negative answer for the problem whether the same results are satisfied or not for other geometric means of n -matrices. Mathematics subject classification (2010): Primary 47A64; Secondary 47A63, 47L25.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4ee5b1452e36baedd4c7d7a7c94dc480141d7f56

How researchers see this paper

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In Applied Mathematics

1. Yongdo Lim
2. Jimmie Lawson
3. Miklós Pálfia

In Geometry and Topology

1. Yongdo Lim
2. Jimmie Lawson

Citations in the corpus

• Karcher means and Karcher equations of positive definite operators (2014, background): “The proofs are heavily dependent on property (Y) and Hansen’s inequality and are similar to those of [17, 24].”