On A Diagrammatic Proof of the Cayley-Hamilton Theorem

Abstract

This note concerns a one-line diagrammatic proof of the Cayley-Hamilton Theorem. We discuss the proof's implications regarding the "core truth" of the theorem, and provide a generalization. We review the notation of trace diagrams and exhibit explicit diagrammatic descriptions of the coefficients of the characteristic polynomial, which occur as the n+1 "simplest" trace diagrams. We close with a discussion of diagrammatic polarization related to the theorem.