On some notions of rank for matrices over tracts

Matthew Baker; Noah Solomon; Tianyi Zhang

On some notions of rank for matrices over tracts

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arxiv 2202.02356 v2 pith:PN2U3D6R submitted 2022-02-04 math.CO math.RA

Matthew Baker , Noah Solomon , Tianyi Zhang This is my paper · ORCID

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keywords matricesnotionsrankablebakerbowlerconceptuallydefine

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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.

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