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\end{bmatrix} \right)  \end{equation}  The implications of carrying through the physics made with this tensor without taking the real part were considered. The creation of an electromagnetic tensor is considered. When being used for a metric in the form \begin{equation}  ds^2=  \begin{bmatrix} dt & dx & dy & dz \end{bmatrix}  \begin{bmatrix}  1 & i & j & k \\  i & -1 & k & -j \\  j & -k & -1 & i \\  k & j & -i & -1  \end{equation}  \begin{bmatrix} dt \\ dx \\ dy \\ dz \end{bmatrix}  \end{equation}  Then from explicit calculation it can be shown that an equaivalent matrix gives \begin{equation}  ds^2=  \begin{bmatrix} dt & dx & dy & dz \end{bmatrix}  \begin{bmatrix}  1 & i & j & k \\  i & -1 & 0 & 0 \\  j & 0 & -1 & 0 \\  k & 0 & 0 & -1  \end{equation}  \begin{bmatrix} dt \\ dx \\ dy \\ dz \end{bmatrix}  \end{equation}