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\section{Electromagnetism}  This formulation would require \begin{equation}  \eta^{\mu \nu}=\frac{1}{1+i^2+j^2+k^2} \begin{bmatrix}  1 & i & j & k \\  i & -1 & -k & j\\  j & k & -1 & -i\\  k & -j & i & -1  \end{bmatrix})  \end{equation}