Mathematical Sciences: Matrix and Combinatorial Theory

数学科学：矩阵与组合理论

• 批准号: 9123318
• 负责人: Richard Brualdi
• 金额: $ 32.26万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-05-15 至 1996-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123318&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Matrix; Combinatorial; Theory

This research is concerned with a variety of problems in linear algebra. One of the principal investigators will study the dependency of zero patterns and signs on matrix invariants; error-correcting codes defined by a greedy algorithm; integer lattices generated by combinatorially defined classes of matrices; computational procedures for certain classes of permanents; and the relation of posets to matrices. The other principal investigator will work on non-negative matrices; the related class of M-matrices and their generalizations; scaling of matrices; and inertia theory of matrices. A matrix is a rectangular array with possible entries from a wide variety of rings. This is a field which originated in the nineteenth century as a part of algebra. It is currently very active in view of its many applications and connections with other parts of mathematics and other scientific and technical disciplines.

这项研究涉及到各种各样的问题， 线性代数 其中一名主要研究人员将研究 零模式和符号对矩阵不变量的依赖性; 由贪婪算法定义的纠错码;整数 由组合定义的类生成的格 矩阵.某些类别的 永久性;以及偏序集与矩阵的关系。另 首席研究员将研究非负矩阵; M-矩阵及其推广; M-矩阵的标度 矩阵和矩阵的惯性理论。 矩阵是一个矩形数组，其中可能有来自 各种各样的戒指 这是一个起源于 19世纪作为代数的一部分。 它还很 鉴于其众多的应用和联系， 数学和其他科学技术的其他部分 学科