Norm of the DFT Sinusoids

For $k=l$, we follow the previous derivation to the next-to-last step to get

$$\left<s_k,s_k\right> = \sum_{n=0}^{N-1}e^{j2\pi (k-k) n /N} = N$$

which proves

$$\zbox {\left\Vert\,s_k\,\right\Vert = \sqrt{N}.}$$