Monotonicity of the number of positive entries in nonnegative matrix powers
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.
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1833-5 |