Trace evaluation of matrix determinants and inversion of 4 $\times$ 4 matrices in terms of Dirac covariants

TL;DR

This paper presents methods for calculating determinants and inverses of 4x4 matrices using Dirac covariants, providing useful formulas and approaches for matrix analysis in theoretical physics.

Contribution

It introduces a novel approach to express 4x4 matrices and their inverses in terms of Dirac covariants, enhancing computational techniques in matrix algebra.

Findings

Formulas for determinants based on matrix traces

Representation of 4x4 matrices using Dirac covariants

Explicit calculation of inverse matrices in Dirac covariant form

Abstract

In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$ matrices are expressed in terms of Dirac covariants. The third step is the calculation of the corresponding inverse matrices in terms of Dirac covariants.