On the spectral norm of a doubly stochastic matrix and level-<i>k</i> circulant matrix release_bgfyioe4cjhd3jasvgi4lscyei

Abstract

<jats:title>Abstract</jats:title> 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 <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_spma-2023-0106_eq_001.png" /> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>r</m:mi> </m:math> <jats:tex-math>r</jats:tex-math> </jats:alternatives> </jats:inline-formula>-circulant matrices. Spectral norm of level-<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_spma-2023-0106_eq_002.png" /> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>k</m:mi> </m:math> <jats:tex-math>k</jats:tex-math> </jats:alternatives> </jats:inline-formula> circulant matrix and applications are given.
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