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Pertubation theory for 3x3 matrix

  1. Sep 15, 2013 #1

    Ton

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    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!
     
  2. jcsd
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