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On probing where this comes from it was postulated that the matrix could be the 'Real' (non-quaternion) part of the outer product of two unit quaternions $Q= w + xi + yj +zk$, \begin{equation}  \eta_{\mu \nu} = Q \otimes Q =Re \Bigg( \left(  \begin{bmatrix}  1 & i & j & k \\  i & -1 & k & -j\\  j & -k & -1 & i\\  k & j & -i & -1  \end{bmatrix} \Bigg) \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.