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