Hyperbolic geometry of positive definite matrices associated with geometric mean

活动时间： 06月24日10时00分       

地            点  ： 数信学院D-417教室

讲座内容：

Hyperbolic geometry of positive definite matrices associated with geometric mean

主讲人介绍：

Dr. Tin-Yau Tam currently serves as the Department Chair of the Department of Mathematics and Statistics at Auburn University. After receiving his PhD from the University of Hong Kong in 1986, he taught in the City University of Hong Kong for two years and then joined Auburn University in 1988 as Assistant Professor and became Associate Professor and Full Professor in 1993 and 1998, respectively. He was honored as Lloyd and Sandra Nix Endowed Professor (2012-15).He has served as Director of Assessment and Planning (2000-2012) in the College of Sciences and Mathematics and Special Assistant to the Provost (2008-2009). He served as a member of the board of directors of the International Linear Algebra Society (2009-2013). Tam’s areas of specialization are Matrix Theory and their Applications, Multilinear Algebra, and Lie Theory. He is the Editor-in-Chief of the Alabama Journal of Mathematics and serves on the editorial boards of Linear and Multilinear Algebra, Electronic Linear Algebra, Special Matrices, and Proyecciones, Revista de Matematica. To date, Tam has authored or coauthored more than ninety research peer-reviewed papers and delivered more than 160 talks. He served as dissertation advisor for six PhD graduates. He now has four PhD students.  

  In this talk we will discuss the geometry and inequalities associated with the geometric mean of positive definite matrices. The space $P_n$ of $n\times n$ positive definite matrices of determinant 1 is a Riemannian manifold. It turns out that the geometry associated with the Riemannian structure is hyperbolic. We show that geodesic convexity emerges when a natural pre-order call log majorization is introduced to $P_n$. We also derive several inequalities for the geometric mean. Some inequalities reflect the hyperbolic geometry  

发布时间：2016-06-23 16:33:33