Mathematical Sciences: RUI: Extreme Points of Cones of Positive Semi-definite Matrices with Given Sparsity Pattern

数学科学：RUI：具有给定稀疏模式的正半定矩阵的锥极点

• 批准号: 9007048
• 负责人: Stephen Pierce
• 金额: $ 9.71万
• 依托单位: San Diego State University Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007048&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Extreme; Points

This research is concerned with two projects in matrix theory. For the first project, G is an undirected graph on n vertices and M(G) is an associated convex cone. The principal investigators will examine the structure of the extreme matrices, particularly when M(G) has extreme points of large rank. The second project is concerned with determining the extreme points of a collection of certain semidefinite matrices. They will investigate whether the rank and sparsity pattern alone determine if a matrix is an extreme point. 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 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.

本研究涉及矩阵中的两个项目 理论对于第一个项目，G是n上的无向图 顶点，M（G）是一个相伴的凸锥。校长 研究人员将检查极端的结构， 矩阵，特别是当M（G）有大的极值点时 等级第二个项目涉及确定 半定集合的端点 矩阵他们将调查是否秩和稀疏 模式单独确定矩阵是否是极值点。 矩阵是一个矩形数组，其中可能有以下元素： 各种各样的戒指。这个领域起源于 19世纪是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