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University of Regina Department of Mathematics and Statistics
 

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 mn 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: M-matrices, inverse M-matrices, 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

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics