deletions | additions       diff --git a/test_begin_matrix_kappa__aa__.tex b/test_begin_matrix_kappa__aa__.tex  index 73d5723..fa2d356 100644  --- a/test_begin_matrix_kappa__aa__.tex  +++ b/test_begin_matrix_kappa__aa__.tex 
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test  $$\begin{matrix}  \kappa_{aa}=\frac{\tilde{\kappa}_{aa}-\frac{c_{ab}\tilde{\kappa}_{ba}}{c_{bb}}}{1-\frac{c_{ab}c_{ba}}{c_{aa}c_{bb}}} & \kappa_{ab}=\frac{\tilde{\kappa}_{ab}-\frac{c_{ab}\tilde{\kappa}_{bb}}{c_{bb}}}{1-\frac{c_{ab}c_{ba}}{c_{aa}c_{bb}}} \\  \kappa_{ba}=\frac{\tilde{\kappa}_{ba}-\frac{c_{ab}\tilde{\kappa}_{aa}}{c_{aa}}}{1-\frac{c_{ab}c_{ba}}{c_{aa}c_{bb}}}) \kappa_{ba}=\frac{\tilde{\kappa}_{ba}-\frac{c_{ab}\tilde{\kappa}_{aa}}{c_{aa}}}{1-\frac{c_{ab}c_{ba}}{c_{aa}c_{bb}}}  & \kappa_{bb}=\frac{\tilde{\kappa}_{bb}-\frac{c_{ab}\tilde{\kappa}_{ab}}{c_{aa}}}{1-\frac{c_{ab}c_{ba}}{c_{aa}c_{bb}}} \\ \end{matrix}$$