In a linear, macroscopic theory, the influence of matter on the electromagnetic field is described through more general linear transformation in the space of 2-forms. We call C : Λ Λ 2 ∋ ∋ F ↦ ↦ G ∈ ∈ Λ Λ ( 4 − − 2 ) the constitutive transformation. The role of this transformation is comparable to the Hodge duality transformation. The Maxwell equations in the presence of matter then become: d F = 0 d G = J where the current 3-form J still satisfies the continuity equation d J = 0.