ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Geometry and Order Structure in Matrices and Operators

Wed 11:30–12:00, SW Raadzaal
Hadamard product for the weighted Karcher means
Sejong Kim (Chungbuk National University)

On the open cone of positive definite matrices, the weighted Karcher mean is defined as the unique minimizer of the weighted sum of squares of the Riemannian distances to each of variables. From the recent result called no dice theorem [2], we show that the Hadamard product for weighted Karcher means of permuted tuples of positive definite matrices with fixed weight is bounded by the Hadamard product of given positive matrices. This generalizes the result of T. Ando [1] for commuting positive definite matrices.

  1. T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26 (1979), pp. 203–241.
  2. Y. Lim and M. Pálfia, Weighted deterministic walks and no dice approach for the least squares mean on Hadamard spaces, Bull. London Math. Soc. 46 (2014), pp. 561–570.