In this problem you will establish the correspondence between Equations 6.30 and 6.31.
(a) Diagonalize the matrix

to obtain the matrix M' = SMS^-1 where S^-1 is the unitary matrix whose columns are the (normalized) eigenvectors of M.
(b) Use the binomial expansion to show that lim_N→∞ (M')^N is a diagonal matrix with entries e^-iφ and e^iφ on the diagonal.
(c) Transform back to the original basis to show that

agrees with the matrix in Equation 6.31.

1 - Coin 9/N M = -9/N 1