 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: Shaun Fallat (University of Regina)
Title: A New Approach to Total Positivity
Date: Friday, February 27, 2004
Time: 15:30
Place: Math & Stats Lounge (CW 307.18)
Abstract
The study of totally positive (TP) matrices grew out of two separate
streams of research in the 30's. Gantmacher and Krein began studying
TP matrices as a result of their investigations into oscillations of me
chanical systems (e.g. tridiagonal matrices). Others like Schoenberg
and Karlin were led to TP matrices via their studies in interpolation
theory (e.g. Vandermonde matrices). Karlin continued to encounter
TP matrices in the areas of probability and integral equations. The
aim of this lecture is to revisit some of the early fundamental facts on
TP matrices (eigenvalues, determinantal inequalities, test criteria) and
present new modern proofs (even generalizations in some instances), by
incorporating a relatively new tool known as bidiagonal factorizations.
