Mathematical Sciences: RUI: Matrix Equations, Inertia and Stability

数学科学：RUI：矩阵方程、惯性和稳定性

• 批准号: 8808237
• 负责人: David Carlson
• 金额: $ 2.78万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8808237&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Matrix; Equations

This research will concern itself with several of the core areas of linear algebra: matrix equations, inertia, and stability, which have relevance both to computational linear algebra and to control theory. First the study of conditions for nonsingularity of solutions of Sylvester, Lyapunov, and Riccati matrix equations will be studied. Second the principal investigator plans to study orthogonal solutions of matrix equations. Third the principal investigator plans to study the construction of symmetrizers with specific properties of use in applications. Fourth the principal investigator will study several areas of inertia theory, namely singular inertia theory, inertia theory for Riccati equations, and generalized inertia. Finally the principal investigator will study when positive definite matrices have positive definite and semidefinite images under certain Lyapunov maps.

本研究将涉及线性代数的几个核心领域：矩阵方程、惯性和稳定性，它们与计算线性代数和控制理论都有关联。首先研究了Sylvester、Lyapunov和Riccati矩阵方程解的非奇异性条件。其次，主要研究者计划研究矩阵方程的正交解。第三，主要研究者计划研究具有特定应用性能的对称器的构造。第四，首席研究员将研究惯性理论的几个领域，即奇异惯性理论、Riccati方程惯性理论和广义惯性。最后，研究了正定矩阵在一定的李雅普诺夫映射下何时具有正定像和半正定像。