关于非负整数矩阵的佩伦根和特征向量

IF 1 3区 数学 Q1 MATHEMATICS
Nikita Agarwal , Haritha Cheriyath , Sharvari Neetin Tikekar
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引用次数: 0

摘要

在本文中,我们利用符号动力学技术获得了非负整数矩阵的佩伦根和特征向量的组合表达式。我们将这样一个矩阵与一个多图关联起来,并考虑与之对应的边移。这就产生了一个禁止词集合 F(对应于两个顶点之间不存在边)和一个重复词集合 R(对应于两个顶点之间有多条边)。一般来说,对于给定的禁用词集合 F 和具有预分配乘数的重复词集合 R,我们以多集合的形式构建广义语言。用一个组合表达式枚举这种广义语言中固定长度的词数,就能得到邻接矩阵的佩伦根和特征向量。我们还得到了这种广义语言是边移位语言的条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Perron root and eigenvectors of a non-negative integer matrix

In this paper, we obtain a combinatorial expression for the Perron root and eigenvectors of a non-negative integer matrix using techniques from symbolic dynamics. We associate such a matrix with a multigraph and consider the edge shift corresponding to it. This gives rise to a collection of forbidden words F which correspond to the non-existence of an edge between two vertices, and a collection of repeated words R with multiplicities which correspond to multiple edges between two vertices. In general, for given collections F of forbidden words and R of repeated words with pre-assigned multiplicities, we construct a generalized language as a multiset. A combinatorial expression that enumerates the number of words of fixed length in this generalized language gives the Perron root and eigenvectors of the adjacency matrix. We also obtain conditions under which such a generalized language is a language of an edge shift.

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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
333
审稿时长
13.8 months
期刊介绍: Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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