deletions | additions       diff --git a/section_Alternative_Interpretation_An_important__.tex b/section_Alternative_Interpretation_An_important__.tex  index dd20990..aa3e999 100644  --- a/section_Alternative_Interpretation_An_important__.tex  +++ b/section_Alternative_Interpretation_An_important__.tex 
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This matrix is also an invariant under the transform $T$, whereas the first is not!  We can consider the determinant \begin{equation}  a f  \begin{vmatrix}  k & l\\   o & p  \end{vmatrix}  -a g  \begin{vmatrix}  j & l\\   n & p  \end{vmatrix}  +a h  \begin{vmatrix}  j & k\\   n & o   \end{vmatrix}  -b e  \begin{vmatrix}  k & l\\   o & p  \end{vmatrix}  +b g  \begin{vmatrix}  i & l\\   m & p  \end{vmatrix}  -b h  \begin{vmatrix}  i & k\\   m & o  \end{vmatrix}  +c e  \begin{vmatrix}  j & l\\   n & p  \end{vmatrix}  -c f  \begin{vmatrix}  i & l\\   m & p  \end{vmatrix}  +c h  \begin{vmatrix}  i & j\\   m & n  \end{vmatrix}  -d e  \begin{vmatrix}  j & k\\   n & o   \end{vmatrix}  +d f  \begin{vmatrix}  i & k\\   m & o  \end{vmatrix}  -d g  \begin{vmatrix}  i & j\\   m & n  \end{vmatrix}  \end{equation}     
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