On Norms of Iterations of {0,1}-Matrices
Spectral Theory
2021-12-13 v1 Functional Analysis
Abstract
Let M be a b*b nonzero {0,1}-matrix. Let \rho(M) be its spectral radius and let |M^n| be the norm of its n-th iteration. In the case \rho(M)>1, we see from the spectral radius formula that {|M^n|}_{n=1}^\infty tends to \infty exponentially as n to \infty. In the case \rho(M)=1, {|M^n|}_{n=1}^\infty can be bounded or tend to \infty depending on M. The fine behavior of this sequence is completely characterized in the present paper.
Cite
@article{arxiv.2112.05507,
title = {On Norms of Iterations of {0,1}-Matrices},
author = {Chun Wei and Fan Wen},
journal= {arXiv preprint arXiv:2112.05507},
year = {2021}
}