## A Quest for Positive Definite Matrices in Finite Fields (a work in progress)

- April 20, 2018
- 2:30 p.m.
- LeConte 312

## Abstract

Positive definite matrices make up an interesting and extremely useful subset of Hermitian matrices. These matrices admit a plethora of equivalent statements and properties, one of which is an existence of a unique Cholesky decomposition. We consider whether any of these equivalent statements to having a unique Cholesky can be analogized for matrices over finite fields. We present new definitions for positive definite matrices over finite fields and some equivalences seen to still hold. Currently, results have been shown for finite fields of certain sizes, specifically powers of two and odd powers of primes congruent to 3 mod 4. There will be room for suggestions on how to proceed with the other finite fields and continuing results in the current cases.