Positive-Definite Matrices over Finite Fields
Combinatorics
2022-02-09 v1 Rings and Algebras
Abstract
The study of positive-definite matrices has focused on Hermitian matrices, that is, square matrices with complex (or real) entries that are equal to their own conjugate transposes. In the classical setting, positive-definite matrices enjoy a multitude of equivalent definitions and properties. In this paper, we investigate when a square, symmetric matrix with entries coming from a finite field can be called "positive-definite" and discuss which of the classical equivalences and implications carry over.
Keywords
Cite
@article{arxiv.2202.04012,
title = {Positive-Definite Matrices over Finite Fields},
author = {Joshua Cooper and Erin Hanna and Hays Whitlatch},
journal= {arXiv preprint arXiv:2202.04012},
year = {2022}
}