deletions | additions       diff --git a/Eigenvalues.tex b/Eigenvalues.tex  index f0c4ef7..c53ec52 100644  --- a/Eigenvalues.tex  +++ b/Eigenvalues.tex 
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\end{equation}  Consider the use of an object $|[A_{11},A_{22}]|=A_{11}A_{22}-A_{12}A_{21}$... $|[A_{00},A_{11}]|=A_{00}A_{11}-A_{01}A_{10}$...  Much like a commutator, something like a detutator, represents the determinant of a 2x2 matrix when trace elementsw are inserted. Then for a 3x3 matrix the similar thing \begin{equation}  |[A_{11},A_{22},A_{33}]| |[A_{00},A_{11},A_{22}]|  = |[A_{11},A_{22}]|A_{33}+|[A_{12},A_{23}]|A_{31}+|[A_{13},A_{21}]|A_{32} |[A_{00},A_{11}]|A_{22}+|[A_{01},A_{12}]|A_{20}+|[A_{02},A_{10}]|A_{21}  \end{equation}  The ordering of these being if the matrix were written next to itself, a diagonal shifting along each row.  We can write in summation form \begin{equation}  |[A_{00},A_{11},A_{22}]| = \sum_{i=0}^2 |[A_{0,0+i mod 4},A_{1,1+i mod 4}]|A_{2,2+i mod 4}  \end{equation}