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Benedict Irwin edited Combination.tex
over 9 years ago
Commit id: 77db4e4c645cc31f25c58b7a3bca44fac9ba1c94
deletions | additions
diff --git a/Combination.tex b/Combination.tex
index fb8a546..0c01afc 100644
--- a/Combination.tex
+++ b/Combination.tex
...
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}