Date of Award

12-10-2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

First Advisor

Dr. Zhongshan Li

Abstract

A sign pattern matrix is a matrix whose entries in the set f+;􀀀; 0g.These matrices are used to describe classes of real matrices with matching signs. The study of sign patterns originated with the need to solve certain problems in economics where only the signs of the entries in matrix are known. Since then applications have been found in areas such as communication complexity, neural networks, and chemistry. Currently much work has been done in identifying shared characteristics of real matrices having the same sign pattern. Of particular interest is sign patterns that allow or require particular properties. In this paper I study sign patterns that allow diagonalizabily, as well as the characteristics of certain types of sign patterns.

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