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3.6: Appendices
https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Thermodynamics_and_Statistical_Mechanics_(Arovas)/03%3A_Ergodicity_and_the_Approach_to_Equilibrium/3.06%3A_Appendices
Multiplying the eigenvector equation for $\phi^\alpha$ on the right by $\psi^\beta_j$ and summing over $j$ , and multiplying the eigenvector equation for $\psi^\beta$ on the left by \(\phi^\alp...Multiplying the eigenvector equation for $\phi^\alpha$ on the right by $\psi^\beta_j$ and summing over $j$ , and multiplying the eigenvector equation for $\psi^\beta$ on the left by $\phi^\alpha_i$ and summing over $i$ , and subtracting the two results yields

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