English

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.

Keywords

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}
}