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\end{bmatrix}  \end{equation}  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 $Q= w + xi + yj +zk$, +zk \to 1+i+j+k$,  \begin{equation} \eta_{\mu \nu} = Q \otimes Q =Re \left(  \begin{bmatrix}