The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p -form to a (n − p)-form, where n is the number of dimensions. Here, it takes the 2-form (F) and gives another 2-form (in four dimensions, n − p = 4 − 2 = 2). For the basis cotangent vectors, the Hodge dual is given as (see Hodge star operator § Four dimensions) ⋆ ⋆ ( d x ∧ ∧ d y ) = − − d z ∧ ∧ d t , ⋆ ⋆ ( d x ∧ ∧ d t ) = d y ∧ ∧ d z , and so on. Using these relations, the dual of the Faraday 2-form is the Maxwell tensor, ⋆ ⋆ F = − − B x d x ∧ ∧ d t − − B y d y ∧ ∧ d t − − B z d z ∧ ∧ d t + E x d y ∧ ∧ d z + E y d z ∧ ∧ d x + E z d x ∧ ∧ d y