Matrix Completions, Moments, and Sums of Hermitian Squares

Mihály Bakonyi; Hugo J. Woerdeman

Mihály Bakonyi and Hugo J. Woerdeman

Matrix Completions, Moments, and Sums of Hermitian Squares

In: Princeton Series in Applied Mathematics, 39

Princeton University Press | 2011

https://doi.org/10.1515/9781400840595

Overview
Contents

About this book

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers.

Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics.

The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.

Author information

Mihály Bakonyi (1962-2010) was professor of mathematics at Georgia State University and coauthor of Schur's Algorithm and Several Applications. Hugo J. Woerdeman is professor and head of the Department of Mathematics at Drexel University.

Reviews

This volume is warmly recommended to those students who want to get acquainted with the important field of matrix completion, interpolation and moment problems, having many applications in areas such as electrical engineering, computer science and physics. It will certainly serve also as an indispensable, basic reference for researchers.---László Kérchy, Acta-Scientiarum-Mathematicarum

Frontmatter Free access PDF PDF	i
Contents Free access PDF PDF	vii
Preface Access restricted Content is available PDF PDF	ix
Chapter 1. Cones of Hermitian matrices and trigonometric polynomials Access restricted Content is available PDF PDF	1
Chapter 2. Completions of positive semidefinite operator matrices Access restricted Content is available PDF PDF	69
Chapter 3. Multivariable moments and sums of Hermitian squares Access restricted Content is available PDF PDF	175
Chapter 4. Contractive analogs Access restricted Content is available PDF PDF	257
Chapter 5. Hermitian and related completion problems Access restricted Content is available PDF PDF	361
Bibliography Access restricted Content is available PDF PDF	475
Subject Index Access restricted Content is available PDF PDF	513
Notation Index Access restricted Content is available PDF PDF	517

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Matrix Completions, Moments, and Sums of Hermitian Squares

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