Chapter 6.5, Problem 6.14P

(a)

To determine

Diagonalize the matrix $M=\left(\begin{array}{cc}1& -\phi /N\\ \phi /N& 1\end{array}\right)$.

(b)

To determine

Show that $\underset{N\to \infty }{\lim }{\left(M^{\prime }\right)}^N$ is a diagonal matrix with entries $e^{-i\phi }$ and $e^{i\phi }$ on the diagonal.

(c)

To determine

Show that $\underset{N\to \infty }{\lim }{M}^N=S^{-1}\left[\underset{N\to \infty }{\lim }{\left(M^{\prime }\right)}^N\right]S$.