As a continuation to this question, I took the matrix $C_{2 \times 2}$ which is:

$$C=\left[ \begin{array}{} a& ace^{-\frac{|\phi_1-\phi_2|}{2}}\\ ace^{-\frac{|\phi_1-\phi_2|}{2}} & a \end{array} \right] $$

And I found its eigenvector and eigenvalues which are:

$$v_1 = \left[ \begin{array}{} 1 \\ 1 \end{array} \right] ,v_2 = \left[ \begin{array}{} -1 \\ 1 \end{array} \right] \\ \lambda_1 = a+ace^{-\frac{|\phi_1-\phi_2|}{\rho}},\lambda_2 = a-ace^{-\frac{|\phi_1-\phi_2|}{\rho}} $$

So, it is still not clear to me why the author says that the eigenvectors have the form $e^{in\phi_i}$.

This form doesn't even have the shape of a vector, and I specifically found the eigenvectors, and there isn't any complex component in it.

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  • $\begingroup$ It's absolutely necessary that you put the correct citation for the article you're including here. That's not optional. $\endgroup$ – Marcus Müller Jan 19 '16 at 10:19
  • $\begingroup$ Also, you're still clinging to words. The Eigenvectors you found at least have values from an equidistant sampling of complex oscillations. $\endgroup$ – Marcus Müller Jan 19 '16 at 10:20
  • $\begingroup$ Also, this is still the same question, you even note that. "It's still not clear" is not a valid reason to open a new question, if you don't really ask a new question. $\endgroup$ – Marcus Müller Jan 19 '16 at 10:22
  • $\begingroup$ I agree with @MarcusMüller here: you haven't found an answer to you original question yet, so expand on that question and get an answer that you can accept. $\endgroup$ – Peter K. Jan 19 '16 at 14:15