When the fields are expressed as linear combinations (of exterior products) of basis forms θ, F = 1 2 F p q θ θ p ∧ ∧ θ θ q . the constitutive relation takes the form G p q = C p q m n F m n where the field coefficient functions and the constitutive coefficients are anticommutative for swapping of each one's indices. In particular, the Hodge star operator that was used in the above case is obtained by taking C p q m n = 1 2 g m a g n b ε ε a b p q − − g in terms of tensor index notation with respect to a (not necessarily orthonormal) basis { ∂ ∂ ∂ ∂ x 1 , … … , ∂ ∂ ∂ ∂ x n } in a tangent space V = T p M and its dual basis { d x 1 , … … , d x n } in V ∗ ∗ = T p ∗ ∗ M , having the gram metric matrix ( g i j ) = ( ⟨ ∂ ∂ ∂ ∂ x i , ∂ ∂ ∂ ∂ x j ⟩ ) and its inverse matrix ( g i j ) = ( ⟨ ⟨ d x i , d x j ⟩ ⟩ ) , and ε ε a b p q is the Levi-Civita symbol with ε ε 1234 = 1 . Up to scaling, this is the only invariant tensor of this type that can be defined with the metric.