On the spectral norm of a doubly stochastic matrix and level-k circulant matrix

A simple proof using Birkhoff theorem is given for the result that the spectral norm of a doubly stochastic matrix is 1. We also show that the result generalizes the results of İpek, Bozkurt, and Jiang and Zhou on circulant matrices and rr-circulant matrices. Spectral norm of level-kk circulant matrix and applications are given.