 
Summary: COLLOQUIUM
University of Regina
Department of Mathematics and Statistics
Speaker: Dr. Shaun Fallat
University of Regina, Canada.
Title: Hadamard products, Retractability, and Oppenheim's inequality
Date: Friday, May 11, 2007
Time: 3:30 p.m.
Place: Math & Stats Lounge (CW 307.20)
Abstract
For two m×n matrices A = [aij] and B = [bij], the matrix AB = [aijbij]
is called the Hadamard product of A and B. It has long been known that
the Hadamard product of two positive semidefinite (PSD) matrices is again
PSD. From this fact, many determinantal inequalities have subsequently
been derived about det(A B) when A and B are PSD. One of the most
celebrated inequalities is known as Oppenheim's inequality. For other im
portant positivity classes, such as: Mmatrices, inverse Mmatrices, and to
tally nonnegative matrices closure under Hadamard multiplication no longer
holds, and thus inequalities like Oppenheim's may no longer be valid. On
the other hand, if we specialize to the subsets of these classes that enjoy
