Benedict Irwin edited Combination.tex  over 9 years ago

Commit id: 77db4e4c645cc31f25c58b7a3bca44fac9ba1c94

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If we then have some matrix of individual particle states \begin{equation}  A=\begin{bmatrix}   phi_{11} \phi_{11}  & phi_{12} \phi_{12}  & phi_{13} \phi_{13}  \\ phi_{21} \phi_{21}  & phi_{22} \phi_{22}  & phi_{23} \phi_{23}  \\ phi_{31} \phi_{31}  & phi_{32} \phi_{32}  & phi_{33} \phi_{33}  \end{bmatrix}  \end{equation} 

A^{-1}=\frac{1}{|A|}  \begin{bmatrix}  \begin{vmatrix} phi_{22} \phi_{22}  & phi_{23} \phi_{23}  \\ phi_{32} \phi_{32}  & phi_{33}\end{vmatrix} \phi_{33}\end{vmatrix}  & \begin{vmatrix} phi_{13} \phi_{13}  & phi_{12} \phi_{12}  \\ phi_{33} \phi_{33}  & phi_{32}\end{vmatrix} \phi_{32}\end{vmatrix}  & \begin{vmatrix} phi_{12} \phi_{12}  & phi_{13} \phi_{13}  \\ phi_{22} \phi_{22}  & phi_{23}\end{vmatrix} \phi_{23}\end{vmatrix}  \\ \begin{vmatrix} phi_{23} \phi_{23}  & phi_{21} \phi_{21}  \\ phi_{33} \phi_{33}  & phi_{31}\end{vmatrix} \phi_{31}\end{vmatrix}  & \begin{vmatrix} phi_{11} \phi_{11}  & phi_{13} \phi_{13}  \\ phi_{31} \phi_{31}  & phi_{33}\end{vmatrix} \phi_{33}\end{vmatrix}  & \begin{vmatrix} phi_{13} \phi_{13}  & phi_{11} \phi_{11}  \\ phi_{23} \phi_{23}  & phi_{21}\end{vmatrix} \phi_{21}\end{vmatrix}  \\ \begin{vmatrix} phi_{21} \phi_{21}  & phi_{22} \phi_{22}  \\ phi_{31} \phi_{31}  & phi_{32}\end{vmatrix} \phi_{32}\end{vmatrix}  & \begin{vmatrix} phi_{12} \phi_{12}  & phi_{11} \phi_{11}  \\ phi_{32} \phi_{32}  & phi_{31}\end{vmatrix} \phi_{31}\end{vmatrix}  & \begin{vmatrix} phi_{11} \phi_{11}  & phi_{12} \phi_{12}  \\ phi_{21} \phi_{21}  & phi_{22}\end{vmatrix} \phi_{22}\end{vmatrix}  \end{bmatrix}  \end{equation}