Question

Can the permittivity tensor always be diagonalized?

Answer 1

For an anisotropic medium, permittivity is a symmetric tensor, with elements as ϵijϵij

How can one be sure that it is diagonalizable, if some elements, say ϵxyϵxy and ϵyxϵyx are imaginary

Answer 2

Clearly, then, one cannot locally diagonalize the metric tensor in general (or else every Riemann manifold would be locally isometric to some Euclidean space.