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Pertubation theory for 3x3 matrix

by Ton
Tags: matrix, pertubation, theory
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Ton
#1
Sep15-13, 12:58 PM
P: 2
Some one knows a study material to diagonalize a matrix mass for 3 neutral scalar using perturbation theory like \begin{equation}
M^2=\left(\begin{array}{ccc}
2 \lambda_{\phi} v_{\phi}^2 &\lambda_{\phi \sigma } v_{\phi}v_{\sigma} & \lambda_{\phi\eta} v_{\phi} v_{\eta} \\
\lambda_{\phi \sigma} v_{\phi} v_{\sigma} & 2\lambda_{\sigma} v_{\sigma}^2 & \lambda_{\sigma \eta} v_{\sigma}v_{\eta} \\
\lambda_{ \phi\eta} v_{\phi} v_{\eta} & \lambda_{\sigma \eta} v_{\sigma} v_{\eta} & 2 \lambda_{\eta} v_{\eta}^2

\end{array}\right) .
\end{equation}
with $$v_{\phi}\ll v_{\sigma} \ll v_{\eta}$$ to obtain all, mix, eigenvectors. Thanks!
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