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

Abstract

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.

Keywords

• spectral norm
• doubly stochastic matrices
• circulant matrices
• 15a60
• 15b51