On A Diagrammatic Proof of the Cayley-Hamilton Theorem

Details On A Diagrammatic Proof of the Cayley-Hamilton Theorem On A Diagrammatic Proof of the Cayley-Hamilton Theorem

2009-07-14

arxiv.org/abs/0907.2364v1

Mathematics

Rings and Algebras

Scientific paper

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.

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