与某些允许或要求对角化的图相关联的符号模式

IF 0.7 4区 数学 Q2 Mathematics
Sunil Das
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引用次数: 0

摘要

表征允许或要求对角化的符号模式矩阵的问题大多是开放的。在本文中,我们引入了树符号模式矩阵的本质索引的概念,并用它来研究图为树的符号模式矩阵对角化的允许问题。我们刻画了允许对角化的符号模式矩阵,其图是星形或路径。我们还给出了图为树的符号模式矩阵允许对角化的一个充分条件。此外,我们给出了符号模式矩阵需要对角化的一个必要条件,并刻画了所有需要对角化性的星形符号模式矩阵。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sign patterns associated with some graphs that allow or require diagonalizability
The problems of characterizing sign pattern matrices that allow or require diagonalizability are mostly open. In this paper, we introduce the concept of essential index for a tree sign pattern matrix and use it to investigate the allow problem on diagonalizability for sign pattern matrices having their graphs as trees. We characterize sign pattern matrices allowing diagonalizability, whose graphs are star or path. We also give a sufficient condition for sign pattern matrices whose graphs are trees to allow diagonalizability. Further, we give a necessary condition for a sign pattern matrix to require diagonalizability and characterize all star sign pattern matrices that require diagonalizability.
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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