Matrix Completions, Moments, and Sums of Hermitian Squares

• Main Authors: Bakonyi, Mihály, Woerdeman, Hugo J
• Format: eBook Book
• Language: English
• Published: Princeton, N.J Princeton University Press 2011
• Edition: 1
• Series: Princeton Series in Applied Mathematics
• Subjects: Algebras, Linear; banded case; Bernstein-Szeg ő measures; Carathéodory problem; chordal case; Christoel-Darboux formulas; completion problems; complex function theory; cones; contractive completion; contractive completions; control theory; Corona problem; electrical engineering; Fejéer-Riesz factorization; Fejér-Riesz factorization; General Topics for Engineers; Hamburger problem; Hermitian forms; Hermitian matrices; Hermitian matrix expressions; Hermitian squares problems; Hermitian structures; Hilbert spaces; Hilbert-Schmidt norm control; linear algebra; MATHEMATICS; MATHEMATICS / Matrices; MATLAB codes; Matrices; measure theory; minimal rank completions; multivariables; Nehari problem; Nevanlinna-Pick problem; operator theory; partial operator matrices; positive Carathéodory interpolation; positive definite completions; positive semidefinite completion; quantum information; Schur complement; semidefinite completions; semidefinite matrices; semidefinite operator matrices; semidefinite programming; separability problem; signal processing; Toeplitz case; Toeplitz matrices; trigonometric polynomials; complex function theory; partial operator matrices; positive semidefinite completion; contractive completion; control theory; mathematics; signal processing; Hilbert–Schmidt norm control; multivariables; MATLAB codes; measure theory; electrical engineering; semidefinite matrices; Fejéer–Riesz factorization; Hermitian matrices; minimal rank completions; semidefinite programming; completion problems; separability problem; banded case; Christoel–Darboux formulas; Nehari problem; cones; Nevanlinna–Pick problem; positive definite completions; Schur complement; positive Carathéodory interpolation; operator theory; Fejér–Riesz factorization; linear algebra; Hilbert spaces; Toeplitz case; semidefinite completions; Carathéodory problem; quantum information; Hamburger problem; Bernstein–Szeg ő measures; chordal case; semidefinite operator matrices; Corona problem; trigonometric polynomials; Hermitian squares problems; contractive completions; Toeplitz matrices; Hermitian matrix expressions; Christoel-Darboux formulas; Hilbert-Schmidt norm control; Fejéer-Riesz factorization; Fejér-Riesz factorization; Bernstein-Szeg ő measures; Nevanlinna-Pick problem
• ISBN: 9780691128894; 0691128898; 1400840597; 9781400840595
• DOI: 10.1515/9781400840595

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.