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Following the steps as in the theoretical treatment of perturbation theory, find eigenvectors and eigenvalues of the matrix $$\left[ \begin{array}{rrr} 1&\epsilon& 0 \\ \epsilon & 1 &-\epsilon \\ 0 & -\epsilon& 2 \end{array}\right] $$ up to the lowest non-vanishing order in $\epsilon$
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4727:Diamond Point
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