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Benedict Irwin edited Complex.tex
over 9 years ago
Commit id: 51ced61e8747585f726ccd4921e75f7e873fbc9f
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diff --git a/Complex.tex b/Complex.tex
index 7c10adf..0c089d5 100644
--- a/Complex.tex
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...
u_2=A_{21}v_2
\end{equation}
At this stage one might consider approaching a matrix like $\mat{1}{1}{1}{1}$...
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} \\
\vec{x_1}{x_2}=\mat{1}{1}{1}{-1}\#\vec{2x_1+x_2}{x_1+x_2}
\end{equation}