Riemannian Mean of Positive Definite Matrices


August 2, 2012


Rajendra Bhatia


Indian National Science Academy


Positive definite matrices arise in several contexts: quantum mechanics, statistics, machine learning, image processing, elasticity etc. Various notions of averaging are useful in different contexts. In the 1970’s physicists, electrical engineers, and matrix theorists developed a notion of a geometric mean of two positive definite matrices. The problem of extending the concept to more than two matrices remained open for several years. The problem was resolved in 2004 using ideas from Riemannian geometry. Meanwhile, effective use of the idea has been made in applications in radar data processing and imaging of the brain. In this talk, I will explain the main ideas from the perspective of matrix analysis.

Reference: R. Bhatia, Positive Definite Matrices, Princeton University Press 2007, Hindustan Book Agency 2007.


Rajendra Bhatia

Rajendra Bhatia did his BSc and MSc from the University of Delhi and his PhD from the Indian Statistical Institute. He was a Reader at the University of Bombay from 1981 to 1984 , after which he joined the Indian Statistical Institute, Delhi, where he is now a distinguished Scientist.