## The 20th Statistical Machine Learning Seminar (2014.10.3)

The 20th Statistical Machine Learning Seminar

Date/time: Oct 3 (Fri) 15:00-

Place: Seminar Room 5 (3F, D313),

Institute of Statistical Mathematics (Tachikawa, Tokyo)

Access: http://www.ism.ac.jp/access/index_e.html

Title: Riemannian geometry and matrix geometric means

Speaker: Professor Rajendra Bhatia

Indian Statistical Institute, New Delhi

Abstract:

Positive definite matrices are used in several areas of mathematics,

physics, statistics and engineering. Often it is required to define an

average of several such matrices that must have some properties dictated by

the problem. One such average is the geometric mean. For two positive

definite matrices the concept was introduced and studied long ago. For more

than two matrices a good definition (based on Riemannian geometry) was given

only ten years ago. Since then there have been many interesting

developments, and the concept has found many applications. In this talk we

will survey these ideas.