On Norms of Iterations of 0,1-Matrices

2021/12/09 by Wei, Chun, Wen, Fan
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2112.05507

Abstract

Let M be a b*b nonzero 0,1-matrix. Let ρ(M) be its spectral radius and let |Mⁿ| be the norm of its n-th iteration. In the case ρ(M)>1, we see from the spectral radius formula that |Mⁿ|_n=1^∞ tends to ∞ exponentially as n to ∞. In the case ρ(M)=1, |Mⁿ|_n=1^∞ can be bounded or tend to ∞ depending on M. The fine behavior of this sequence is completely characterized in the present paper.

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