deletions | additions       diff --git a/Complex.tex b/Complex.tex  index 0c089d5..c7ad35b 100644  --- a/Complex.tex  +++ b/Complex.tex 
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However, the normal determinant is zero! When we get the resulting transformed vector both elements will equal $x_1+x_2$ and are indistinguishable, there is no way to know the order $x_1$ and $x_2$ should be sorted back! (NB. Think about the relavance with quantum indistinguishability here...). Instead consider the non-singular matrix \begin{equation}  \mat{2}{1}{1}{1}\vec{x_1}{x_2}=\vec{x_1+x_2}{x_2} \\  \frac{1}{3}\mat{1}{1}{1}{-1}\#\mat{2}{1}{1}{1}\vec{x_1}{x_2}=\fraac{1}{3}\mat{1}{1}{1}{-1}\#\vec{2x_1+x_2}{x_1+x_2} \frac{1}{3}\mat{1}{1}{1}{-1}\#\mat{2}{1}{1}{1}\vec{x_1}{x_2}=\frac{1}{3}\mat{1}{1}{1}{-1}\#\vec{2x_1+x_2}{x_1+x_2}  \\ \vec{x_1}{x_2}=\mat{1}{1}{1}{-1}\#\vec{2x_1+x_2}{x_1+x_2}  \end{equation}