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.
