The $4 \times 4$ minors of a $5 \times 5$ symmetric matrix are a tropical basis

TL;DR

This paper proves that the set of all $4 imes 4$ minors of a $5 imes 5$ symmetric matrix forms a tropical basis, advancing understanding of tropical algebraic geometry.

Contribution

It establishes that the $4 imes 4$ minors of a symmetric matrix constitute a tropical basis, a previously unresolved question in tropical geometry.

Findings

$4 imes 4$ minors form a tropical basis for symmetric matrices

Advances understanding of tropical algebraic geometry

Provides a foundation for further research in tropical matrix theory

Abstract

This paper proves the $4 \times 4$ minors of a $5 \times 5$ symmetric matrix of indeterminates are a tropical basis.