Benedict Irwin edited Combination.tex  over 9 years ago

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\section{Combination}  If we then have some matrix of individual particle states. states \begin{equation}  A=\begin{bmatrix}   phi_{11} & phi_{12} & phi_{13} \\ phi_{21} & phi_{22} & phi_{23} \\ phi_{31} & phi_{32} & phi_{33}  \end{bmatrix}  \end{equation}  we can calculate the inverse as \begin{equation}  A^{-1}=\frac{1}{|A|}  \begin{bmatrix}  \begin{vmatrix} phi_{22} & phi_{23} \\ phi_{32} & phi_{33}\end{vmatrix} &  \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} &  \begin{vmatrix} phi_{11} & phi_{13} \\ phi_{31} & phi_{33}\end{vmatrix} &  \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} &  \begin{vmatrix} phi_{11} & phi_{12} \\ phi_{21} & phi_{22}\end{vmatrix}   \end{bmatrix}  \end{equation}