English

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}
}
R2 v1 2026-06-24T09:26:49.237Z