Fermionic matrices and super Cayley--Hamilton algebras

TL;DR

This paper extends classical matrix theorems to graded algebraic structures involving both bosonic and fermionic matrices, establishing foundational results for super Cayley--Hamilton algebras.

Contribution

It introduces graded analogues of fundamental theorems for matrices, specifically for bosonic and fermionic cases, advancing the theory of super Cayley--Hamilton algebras.

Findings

Established first and second fundamental theorems for graded matrix tuples

Developed graded analogues of classical matrix theorems

Enhanced understanding of super Cayley--Hamilton algebra structures

Abstract

We develop a first and second fundamental theorem for $n$--tuples of bosonic and fermionic matrices, by developing graded analogues of the classical case.