Journal of Inequalities and Applications (Sep 2018)
Monotonicity of the number of positive entries in nonnegative matrix powers
Abstract
Abstract Let A be a nonnegative matrix of order n and f(A) $f(A)$ denote the number of positive entries in A. We prove that if f(A)≤3 $f(A)\leq3$ or f(A)≥n2−2n+2 $f(A)\geq n^{2}-2n+2$, then the sequence {f(Ak)}k=1∞ $\{f(A^{k})\}_{k=1}^{\infty}$ is monotonic for positive integers k.
Keywords