17.12.2010

Christmas Lecture
=================
Jan Brandts (University of Amsterdam, The Netherlands)

Linear Algebra and Geometry of Completely Positive Matrices

Summary:
========
A matrix B is called completely positive if B=VV^t  for some
nonnegative matrix V. Necessary conditions for B to be com-
pletely positive are that B is both positive semi-definite and
nonnegative, but these conditions are not sufficient if B has
size 5x5 or larger.

In this presentation we review properties of and theorems on
completely positive matrices, which include geometric inter-
pretations of complete positivity. A second type of matrices
that pops up are the so-called ultrametric matrices.