Combinatorial and spectral analysis of matrix patterns

矩阵模式的组合和谱分析

• 批准号: 203336-2011
• 负责人: VanderMeulen, Kevin
• 金额: $ 0.73万
• 依托单位: Redeemer University College
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=523437
• 关键词: Combinatorial; spectral; analysis; matrix; patterns

The proposed research explores the interplay between two different areas of mathematics, namely linear algebra and graph theory. One particular type of problem being explored is how mathematics on arrays of numbers is affected by qualitative information, such as the pattern of positive, negative and zero entries in the array. Sometimes this information alone is sufficient to observe significant restrictions on results, independent of the magnitude of the individual numbers in the array. These sign patterns can be modeled using graph theory and this theory can provide insights into the restrictions for given patterns. Part of this research entails determining what restrictions can be discovered with these models, and likewise, how these models can help demonstrate lack of restrictions.

拟议的研究探讨了两个不同的数学领域之间的相互作用，即线性代数和图论。 正在探索的一个特殊类型的问题是，数字数组上的数学如何受到定性信息的影响，例如数组中正、负和零条目的模式。有时，仅此信息就足以观察到对结果的显著限制，而与数组中单个数字的大小无关。这些符号模式可以使用图论建模，并且该理论可以提供对给定模式的限制的见解。这项研究的一部分需要确定可以用这些模型发现哪些限制，以及这些模型如何帮助证明缺乏限制。