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Dispersion relation for anisotropic media

The electromagnetic wave propagation in an anisotropic dielectric media with two generic matrices $ε^{ij}$ and $μ^{ij}$ of permittivity and permeability is studied. These matrices are not required to be symmetric, positive definite, and even invertible. In the framework of a metric-free electrodynamics approach, compact tensorial dispersion relation is derived. The resulted formula are useful for a theoretical study of electromagnetic wave propagation in a classical media and in a modern type of media with a generic linear constitutive relation including metamaterials.