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

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.