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 it's eigen vector 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 sais that the eigenvectors has the form $e^{in\phi_i}$. I mean, this form doesn't even have a form of a vector... and I specifically found the eigenvectors, and there isn't any complex component in it. Clearly I am missing something very crucial and basic here..
any help? Thanks!
