Showing that any type- \((2,0)\) tensor field \(\mathtt {T}\) , derived from a set of source 3-forms \(\{ \tau ^{r}_{a}\}\) (Sect. 20.3 ), is symmetric is an algebraic process relying on the form structure of the elements in the set. In Chap. 21 , we illustrate this process (in detail) for the Maxwell stress-energy-momentum tensor \(\mathtt {T}^{(\text{MAX})}\) using the properties of the Hodge map and exterior algebra. The components \(\mathtt {T}^{(\text{MAX})}_{ab}\) are then expressed in any spacetime basis and, for any observer field V , we show that there exists a positive, instantaneous electromagnetic energy density associated with \(\mathtt {T}^{(\text{MAX})}\) , in any arbitrary spacetime metric \(\mathtt {g}\) . The tensor is shown to have a vanishing \(\mathtt {g}\) -trace and, if F and \(\mathtt {g}\) satisfy the Einstein-Maxwell field equations without current sources, the spacetime Ricci tensor is shown to satisfy \(\mathtt {Ric}(V,V)\geq 0\) for all observers V . For field systems where F is coupled to a non-zero current 3-form source \(\mathcal {J}\) , we exploit the covariant exterior derivative \(\mathfrak {D}\) to express the Maxwell stress 3-forms \(\{\tau ^{(\text{MAX})}_{a}\}\) in terms of F and \(\mathcal {J}\) .