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

该奖项支持学院的Leiba Rodman教授 威廉和玛丽将继续进行富有成效的合作， 数学教授A。C. M. Ran，M. A. Kaashoek和 I.荷兰阿姆斯特丹自由大学的Gohberg说。 他们正在几个相互关联的研究课题上合作 在系统和控制的一般领域。 共同的主题是 有理矩阵值矩阵不变子空间的研究 功能以及它们之间的相互关系。 更具体地说， 提出的研究问题包括扰动分析， 不变空间，对称分解和插值 对称有理矩阵函数，以及 真实的反对称有理矩阵函数。 拟议的工作是在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 将导致更好地理解的不变子空间 矩阵（一般和特殊类）和几个 自伴和 反对称矩阵函数 这两个主题是相互关联的， 并构成了正在进行的研究的一个重要组成部分， 受现代数学的启发和应用， 电气工程

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.