谱界的矩阵实现

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2025-04-23 DOI:10.1016/j.jctb.2025.04.006

Yen-Jen Cheng , Chih-wen Weng

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引用次数: 0

摘要

利用非负矩阵的修正商矩阵，给出了求非负矩阵最大实特征值界的统一、系统的方法。我们利用这一见解来识别唯一矩阵，其最大实特征值在所有(0,1)-具有指定数量的矩阵中是最大的。这一结果解决了R. Brualdi和a . Hoffman以及F. Friedland在1985年独立提出的一个问题。

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A matrix realization of spectral bounds

We give a unified and systematic way to find bounds for the largest real eigenvalue of a nonnegative matrix by considering its modified quotient matrix. We leverage this insight to identify the unique matrix whose largest real eigenvalue is maximum among all

(0, 1)

-matrices with a specified number of ones. This result resolves a problem that was posed independently by R. Brualdi and A. Hoffman, as well as F. Friedland, back in 1985.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.