4 x 4 matrices in Dirac parametrization: inversion problem and determinant

TL;DR

This paper investigates the parametrization of complex 4x4 matrices using Dirac tensor parameters, providing solutions for matrix inversion and explicit formulas for determinants.

Contribution

It introduces a Dirac tensor parametrization for 4x4 matrices and derives explicit formulas for their inversion and determinants, advancing mathematical tools for matrix analysis.

Findings

Explicit inversion formula for 4x4 matrices in Dirac parametrization

Determinant expression in terms of Dirac parameters

Enhanced understanding of matrix parametrization techniques

Abstract

Parametrization of complex 4 x 4 - matrices G in terms of Dirac tensor parameters (A,B,A_{l},B_{l},F_{kl}) or equivalent four complex 4-vectors (k,m,n,l) is investigated. In the given parametrization, the problem of inverting any 4 x 4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F(k,m,n,l).