 Index conventions for the electromagnetic field tensor

Choose coordinates $x^{\mu }=(ct,\mathbf{x})$ and Minkowski metric $\eta =\mathrm{diag}(1,-1,-1,-1)$. With the convention $F^{0i}=-E_i/c$ and $F^{ij}=-{ϵ}_{ijk}{B}_k$, lowering both tensor indices gives $F_{0i}=+E_i/c$ while leaving $F_{ij}=F^{ij}$. An array with all upper indices cannot be used unchanged as the corresponding array with all lower indices. The propagation Lorentz four-vector $n^{\mu }=(1,\mathbf{s})$ for unit spatial direction $\mathbf{s}$ similarly has $n_{\mu }=(1,-\mathbf{s})$. These signs matter in contractions that encode Maxwell equations.