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This version of SharkBytes has been archived as of February 28, 2019. To search through archived articles, visit nova.edu/search. To access the new version of SharkBytes, visit sharkbytes.nova.edu.

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3301 College Avenue
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Contact

Division of Public Relations and Marketing Communications
Nova Southeastern University
3301 College Avenue
Fort Lauderdale, Florida 33314-7796

(954) 262-5353
(800) 541-6682 x25353
Fax: (954) 262-3954
communications@nova.edu

Halmos Lecture Series Focuses on Eigenvalues, March 1

Math li

Zhongshan Li, Ph.D.

On Friday, March 1, the Mathematics Colloquium Series will present Zhongshan Li, Ph.D.’s lecture, “Irreducible sign patterns that require all distinct eigenvalues”. Hosted by Halmos College’s Department of Mathematics, this lecture will look at eigenvalues. Li is the Graduate Director of Mathematics at Georgia State University.

The research discussed will include a sign pattern (matrix) is a matrix whose entries are from the set {+, -, 0}. Li states, “We say that a sign pattern A requires a certain matrix property P if every real matrix whose entries have signs agreeing with A has the property P. Some necessary or sufficient conditions for a square sign pattern to require all distinct eigenvalues are presented. Characterization of such sign pattern matrices is equivalent to determining when a certain real polynomial takes on only positive values whenever all of its variables are assigned arbitrary positive values. It is known that such sign patterns require a fixed number of real eigenvalues. The 3×3 irreducible sign patterns that require 3 distinct eigenvalues have been identified previously. We characterize the 4×4 irreducible sign patterns that require four distinct real eigenvalues and those that require four distinct nonreal eigenvalues. The 4×4 irreducible sign patterns that require two distinct real eigenvalues and two distinct nonreal eigenvalues are investigated.”

This lecture will take place in Parker 301 from 12:05-12:55. For more information, please contact Colloquium organizer Fuzhen Zhang at zhang@nova.edu.