This thesis aims to study criteria for diagonalizability over finite fields. First we review basic and major results in linear algebra, including the Jordan Canonical Form, the Cayley-Hamilton theorem, and the spectral theorem; the last of which is an important criterion for for matrix diagonalizability over fields of characteristic 0, but fails in finite fields. We then calculate the number of diagonalizable and non-diagonalizable 2x2 matrices and 2x2 symmetric matrices with repeated and distinct eigenvalues over finite fields. Finally, we look at results by Brouwer, Gow, and Sheekey for enumerating symmetric nilpotent matrices over finite fields.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Marks, Theophilus K.

Publisher

• Worcester Polytechnic Institute

Identifier

• 22726
• E-project-050621-093654

Keyword

• Abstract Algebra
• Matrices
• Algebra
• Diagonalization
• Finite Fields

Advisor

• Keane, Patrick Gerard

Year

• 2021

Date created

• 2021-05-06

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright