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\end{equation}  There is now a huge level of symmetry.  Making a transition from $aa\to bb$, where $aThus we now have a transform for a $4\times4$ matrix as \begin{equation}  M=\begin{bmatrix}  m_{00} & m_{01} & m_{02} & m_{03} \\  m_{10} & m_{11} & m_{12} & m_{13} \\  m_{20} & m_{21} & m_{22} & m_{23} \\  m_{30} & m_{31} & m_{32} & m_{33}  \end{bmatrix}  \\  T(M)=  \begin{bmatrix}  m_{00} & m_{01} & m_{10} & m_{11} \\  m_{02} & m_{03} & m_{12} & m_{13} \\  m_{20} & m_{21} & m_{30} & m_{31} \\  m_{22} & m_{23} & m_{32} & m_{33}  \end{bmatrix}  \end{equation}