On some notions of rank for matrices over tracts

TL;DR

This paper introduces multiple notions of matrix rank over tracts, unifying various existing concepts and providing clearer proofs for related results in the literature.

Contribution

It defines several rank notions for matrices over tracts, unifying and clarifying existing results with conceptually satisfying proofs.

Findings

Multiple rank notions are introduced for matrices over tracts.

Unified framework simplifies understanding of matrix ranks over tracts.

Provides clearer proofs for known results in the literature.

Abstract

Given a tract $F$ in the sense of Baker and Bowler and a matrix $A$ with entries in $F$, we define several notions of rank for $A$. In this way, we are able to unify and find conceptually satisfying proofs for various results about ranks of matrices that one finds scattered throughout the literature.