Spectrally Arbitrary Patterns

Document Type

Presentation Abstract

Presentation Date

11-19-2018

Abstract

A sign pattern is a matrix whose entries are from the set {0,+,−}, while a zero-nonzero pattern is a matrix whose entries are from the set {0,∗}. The idea behind sign and zero-nonzero patterns came from need to solve problems in economics (and other areas) when only the signs of the entries in a matrix are known. Sign and zero-nonzero patterns are areas of interest in qualitative matrix theory and, due to the connections with graph theory, combinatorial matrix theory. In this talk, we will discuss some background information about patterns before focusing on spectrally arbitrary patterns. We will go through a few techniques on how to determine if a pattern is spectrally arbitrary, including some techniques based on algebraic properties of rings and fields.

Additional Details

Monday, November 19, 2018 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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