Recent Advances in Matrix and Operator Theory

This book expands the lectures given at IWOTA’05 (International Workshop on Operator Theory and Applications) which was held at the University of Connecticut, Storrs, USA, July 24–27, 2005. Many developments on the cutting edge of research in operator theory, matrix theory, coding theory, system theory, control theory and numerical linear algebra are reflected in this collection of original articles.

The volume is of a cross-disciplinary nature. A number of papers are devoted to the analysis and algorithms for matrices with quasiseparable structure which is an active area of concurrent research in numerical linear algebra.

Inverse Problems for First-Order Discrete Systems.- Stability of Dynamical Systems via Semidefinite Programming.- Ranks of Hadamard Matrices and Equivalence of Sylvester—Hadamard and Pseudo-Noise Matrices.- Image of a Jacobi Field.- The Higher Order Carathéodory—Julia Theorem and Related Boundary Interpolation Problems.- A Generalization to Ordered Groups of a Kre?n Theorem.- A Fast QR Algorithm for Companion Matrices.- The Numerical Range of a Class of Self-adjoint Operator Functions.- A Perturbative Analysis of the Reduction into Diagonal-plus-semiseparable Form of Symmetric Matrices.- The Eigenstructure of Complex Symmetric Operators.- Higher Order Asymptotic Formulas for Traces of Toeplitz Matrices with Symbols in Hölder-Zygmund Spaces.- On an Eigenvalue Problem for Some Nonlinear Transformations of Multi-dimensional Arrays.- On Embedding of the Bratteli Diagram into a Surface.- Superfast Inversion of Two-Level Toeplitz Matrices Using Newton Iteration and Tensor-Displacement Structure.- On Generalized Numerical Ranges of Quadratic Operators.- Inverse Problems for Canonical Differential Equations with Singularities.- On Triangular Factorization of Positive Operators.- Solutions for the H ?(Dn) Corona Problem Belonging to exp(L1/2n-1.- A Matrix and its Inverse: Revisiting Minimal Rank Completions.