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Error propagation in Amplitude Analysis (view source)
Revision as of 18:56, 22 November 2011
, 18:56, 22 November 2011no edit summary
I = \sum_{\alpha\beta}^n{
I = \sum_{\alpha\beta}^n{
\left(\begin{array}{lr}a_\alpha & b_\beta\end{array}\right)
\left(\begin{array}{lr}a_\alpha & b_\beta\end{array}\right)
\left(\begin{array}{lr}\Re{I}_{\alpha\beta} &-\Im{I}_{\alpha\beta}
\left(\begin{array}{lr}\Re(I_{\alpha\beta}) &-\Im(I_{\alpha\beta})
\\ \Im{I}_{\alpha\beta} & \Re{I}_{\alpha\beta}
\\ \Im(I_{\alpha\beta}) & \Re(I_{\alpha\beta})
\end{array}\right)
\end{array}\right)
\left(\begin{array}{c}a_\alpha \\ b_\beta\end{array}\right)
\left(\begin{array}{c}a_\alpha \\ b_\beta\end{array}\right)
}
}
</math>
</math>
:<math>
= \sum_{\alpha\beta}^{2n}{a_\alpha b_\beta J_{\alpha\beta}}
</math>
where the sum over ''n'' complex parameters is expanded to a sum over 2''n'' real ones, and the matrix ''J'' represents the above ''2n''x''2n'' matrix of the elements of ''I''.
<math>
<math>