On the Cayley-Hamilton Theorem for Supermatrices

TL;DR

This paper proposes a conjecture relating the Cayley-Hamilton theorem coefficients for supermatrices to supertraces, supported by tests on various dimensions and supplemented with generating functions.

Contribution

It introduces a new conjecture connecting supermatrix coefficients with supertraces and provides methods to compute these coefficients.

Findings

Conjecture tested successfully on multiple supermatrix dimensions

Generated functions for coefficient determination provided

Unique results obtained for specific supermatrix cases

Abstract

We present a conjecture for expressing the coefficients in the Cayley-Hamilton theorem for supermatrices in terms of supertraces. The conjecture is tested for several supermatrix dimensions and unique results are obtained. Generating functions for determining these coefficients are also given.