Dispersion relation for electromagnetic waves in anisotropic media

Electromagnetic wave propagation in anisotropic dielectric media with two generic matrices εijεij and μijμij of permittivity and permeability is studied. In the framework of a metric-free electrodynamics approach, a compact tensorial dispersion relation is derived. The derivation does not require the corresponding matrices to be symmetric, positive definite, nor even invertible. The resulting formula is useful for a theoretical and experimental study of electromagnetic wave propagation in a wide class of linear media.