U.S.-Netherlands Cooperative Research on Invariant Subspacesand Factorization of Rational Matrix Functions (Mathematics)

该奖项支持威廉与玛丽学院的Leiba Rodman教授与荷兰阿姆斯特丹自由大学的a . C. M. Ran、M. a . Kaashoek和I. Gohberg教授在数学领域继续进行卓有成效的合作。他们在系统和控制的一般领域共同研究几个相互关联的课题。一般的主题是研究矩阵的不变子空间、有理矩阵值函数及其相互关系。具体来说，提出的研究问题包括不变空间的摄动分析、对称有理矩阵函数的对称分解与插值、实偏对称有理矩阵函数的极小分解。所提出的工作是一个高度活跃的数学领域，涉及线性代数和经典算子理论。结果将导致更好地理解矩阵（一般和特殊类）的不变子空间以及自伴随和偏对称矩阵函数的几个插值和分解问题。这两个主题是相互关联的，并且构成了受现代电气工程启发并应用于现代电气工程的数学发展领域正在进行的研究的重要组成部分。

This award supports Professor Leiba Rodman of the College of William and Mary to continue a highly productive collaboration in mathematics with Professors A. C. M. Ran, M. A. Kaashoek, and I. Gohberg, of the Vrije University, Amsterdam, The Netherlands. They are working together on several interrelated research topics in the general area of systems and control. The common theme is a study of invariant subspaces of matrices, rational matrix valued functions and the interrelations between them. More specifically, the proposed research problems include perturbation analysis of invariant spaces, symmetric factorization and interpolation of symmetric rational matrix functions, and minimal factorizations of real skew-symmetric rational matrix functions. The proposed work is in a highly active area of mathematics involving linear algebra and classical operator theory. Results will lead to a better understanding of invariant subspaces of matrices (both general and special classes) and of several interpolation and factorization problems for self-adjoint and skew-symmetric matrix functions. These two topics are interrelated, and comprise an important part of the ongoing research of a developing field of mathematics inspired by and applied to modern electrical engineering.