Document Type

Paper

Publication Date

Spring 2023

Abstract

In this paper, we investigate the numerical range of matrices over finite fields, particularly triangular matrices. We conjecture that all strictly triangular matrices over finite fields of dimension 3 or greater have a numerical range encompassing the entirety of the finite field. We use both algebraic and computational methods to support this claim, making some concrete progress towards the algebraic proof. Further, we conjecture that all matrices over finite fields have a numerical range falling into one of five potential categories, providing an extensive appendix of randomly generated computational examples which seems to support this conjecture.

Notes

Course: MAT 450, Directed Research (Dr. Derek Thompson)

Funding Source: Women's Giving Circle Grant

Published in the Ball State University, Mathematics Exchange (Vol. 16, No. 1, Fall 2022, pgs. 104-120, https://digitalresearch.bsu.edu/mathexchange).

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