On limits of powers of certain absolutely row-stochastic matrices

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• 作者：Steffen Eger ^{eger.steffen@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15B51 ; 15B48 ; 05C50 ; 05C57 ; 05C81 ; 60J10
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 November 2016
• 年：2016
• 卷：508
• 期：Complete
• 页码：1-13
• 全文大小：364 K

文摘

We consider limits of powers of matrices that are absolutely row-stochastic — matrices A such that |A|$|\mathbf{A}|$ is row-stochastic. We give graph theoretic criteria when such limits exist, and if so, determine their value. In particular, we show that for aperiodic connected matrices that satisfy ‘+-opposition bipartiteness’ (+OBIPness) a ‘Perron–Frobenius property’ holds. Here, we call A +OBIP (also called structural balance in the literature) when nodes in the graph corresponding to A can be partitioned into two groups such that within-group links are non-negative and across-group links are non-positive.