Constitutive relations for electromagnetic field in a form of $6\times 6$ matrices derived from the geometric algebra

Abstract: To have a closed system, the Maxwell equations should be supplemented by constitutive relations which connect the primary electromagnetic fields $(\bE,\bB)$ with the secondary ones $(\bD,\bH)$ induced in a medium. Recently [Opt. Commun. \textbf{354}, 259 (2015)] the allowed shapes of the constitutive relations that follow from the relativistic Maxwell equations formulated in terms of geometric algebra were constructed by author. In this paper the obtained general relativistic relations between $(\bD,\bH)$ and $(\bE,\bB)$ fields are transformed to four $6\times 6$ matrices that are universal in constructing various combinations of constitutive relations in terms of more popular Gibbs-Heaviside vectorial calculus frequently used to investigate the electromagnetic wave propagation in anisotropic, birefringent, bianisotropic, chiral etc media.