Monotonicity of the number of positive entries in nonnegative matrix powers

摘要

Let A be a nonnegative matrix of order n and f(A) denote the number of positive entries in A. We prove that if f(A) ≤ 3 or f(A) ≥ n² − 2n + 2, then the sequence {f(Ak)}k=1∞ is monotonic for positive integers k.