Monotonicity of the number of positive entries in nonnegative matrix powers

Let A be a nonnegative matrix of order n and [Formula: see text] denote the number of positive entries in A. We prove that if [Formula: see text] or [Formula: see text] , then the sequence [Formula: see text] is monotonic for positive integers k.

Detalles Bibliográficos
Autor principal: Xie, Qimiao
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6154057/
https://www.ncbi.nlm.nih.gov/pubmed/30839676
http://dx.doi.org/10.1186/s13660-018-1833-5
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author Xie, Qimiao
author_facet Xie, Qimiao
author_sort Xie, Qimiao
collection PubMed
description Let A be a nonnegative matrix of order n and [Formula: see text] denote the number of positive entries in A. We prove that if [Formula: see text] or [Formula: see text] , then the sequence [Formula: see text] is monotonic for positive integers k.
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spelling pubmed-61540572018-10-10 Monotonicity of the number of positive entries in nonnegative matrix powers Xie, Qimiao J Inequal Appl Research Let A be a nonnegative matrix of order n and [Formula: see text] denote the number of positive entries in A. We prove that if [Formula: see text] or [Formula: see text] , then the sequence [Formula: see text] is monotonic for positive integers k. Springer International Publishing 2018-09-21 2018 /pmc/articles/PMC6154057/ /pubmed/30839676 http://dx.doi.org/10.1186/s13660-018-1833-5 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Xie, Qimiao
Monotonicity of the number of positive entries in nonnegative matrix powers
title Monotonicity of the number of positive entries in nonnegative matrix powers
title_full Monotonicity of the number of positive entries in nonnegative matrix powers
title_fullStr Monotonicity of the number of positive entries in nonnegative matrix powers
title_full_unstemmed Monotonicity of the number of positive entries in nonnegative matrix powers
title_short Monotonicity of the number of positive entries in nonnegative matrix powers
title_sort monotonicity of the number of positive entries in nonnegative matrix powers
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6154057/
https://www.ncbi.nlm.nih.gov/pubmed/30839676
http://dx.doi.org/10.1186/s13660-018-1833-5
work_keys_str_mv AT xieqimiao monotonicityofthenumberofpositiveentriesinnonnegativematrixpowers

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