Benedict Irwin edited Combination.tex  over 9 years ago

Commit id: bcc61cf741bb2aa308ec43954e399c3d7e8042cd

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\end{bmatrix}  \end{equation}  We also then know that \begin{equation}  \frac{1}{|A|}  \begin{bmatrix}   \phi_{11} & \phi_{12} & \phi_{13} \\ \phi_{21} & \phi_{22} & \phi_{23} \\ \phi_{31} & \phi_{32} & \phi_{33}  \end{bmatrix}  \begin{bmatrix}  \Psi(r_2,r_3) &  \begin{vmatrix} \phi_{13} & \phi_{12} \\ \phi_{33} & \phi_{32}\end{vmatrix} &  \begin{vmatrix} \phi_{12} & \phi_{13} \\ \phi_{22} & \phi_{23}\end{vmatrix} \\  \begin{vmatrix} \phi_{23} & \phi_{21} \\ \phi_{33} & \phi_{31}\end{vmatrix} &  \Psi(r_1,r_3) &  \begin{vmatrix} \phi_{13} & \phi_{11} \\ \phi_{23} & \phi_{21}\end{vmatrix} \\  \begin{vmatrix} \phi_{21} & \phi_{22} \\ \phi_{31} & \phi_{32}\end{vmatrix} &  \begin{vmatrix} \phi_{12} & \phi_{11} \\ \phi_{32} & \phi_{31}\end{vmatrix} &  \Psi(r_1,r_2)  \end{bmatrix}  =  \begin{bmatrix}  1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1  \end{bmatrix}  \end{equation}