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The Resource Matrix completions, moments, and sums of hermitian squares, Mihály Bakonyi and Hugo J. Woerdeman

Matrix completions, moments, and sums of hermitian squares, Mihály Bakonyi and Hugo J. Woerdeman

Label
Matrix completions, moments, and sums of hermitian squares
Title
Matrix completions, moments, and sums of hermitian squares
Statement of responsibility
Mihály Bakonyi and Hugo J. Woerdeman
Creator
Contributor
Author
Subject
Language
eng
Summary
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
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Cataloging source
N$T
Illustrations
illustrations
Index
index present
Language note
In English
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Princeton series in applied mathematics
Matrix completions, moments, and sums of hermitian squares, Mihály Bakonyi and Hugo J. Woerdeman
Label
Matrix completions, moments, and sums of hermitian squares, Mihály Bakonyi and Hugo J. Woerdeman
Link
http://www.jstor.org/stable/10.2307/j.ctt7rp1d
Publication
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Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 475-512) and indexes
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Cover -- Contents -- Preface -- Chapter 1. Cones of Hermitian matrices and trigonometric polynomials -- 1.1 Cones and their basic properties -- 1.2 Cones of Hermitian matrices -- 1.3 Cones of trigonometric polynomials -- 1.4 Determinant and entropy maximization -- 1.5 Semidefinite programming -- 1.6 Exercises -- 1.7 Notes -- Chapter 2. Completions of positive semidefinite operator matrices -- 2.1 Positive definite completions: the banded case -- 2.2 Positive definite completions: the chordal case -- 2.3 Positive definite completions: the Toeplitz case -- 2.4 The Schur complement and Fej233;r-Riesz factorization -- 2.5 Schur parameters -- 2.6 The central completion, maximum entropy, and inheritance principle -- 2.7 The Hamburger moment problem and spectral factorization on the real line -- 2.8 Linear prediction -- 2.9 Exercises -- 2.10 Notes -- Chapter 3. Multivariable moments and sums of Hermitian squares -- 3.1 Positive Carath233;odory interpolation on the polydisk -- 3.2 Inverses of multivariable Toeplitz matrices and Christoffel-Darboux formulas -- 3.3 Two-variable moment problem for Bernstein-Szeg246; measures -- 3.4 Fej233;r-Riesz factorization and sums of Hermitian squares -- 3.5 Completion problems for positive semidefinite functions on amenable groups -- 3.6 Moment problems on free groups -- 3.7 Noncommutative factorization -- 3.8 Two-variable Hamburger moment problem -- 3.9 Bochners theorem and an application to autoregressive stochastic processes -- 3.10 Exercises -- 3.11 Notes -- Chapter 4. Contractive analogs -- 4.1 Contractive operator-matrix completions -- 4.2 Linearly constrained completion problems -- 4.3 The operator-valued Nehari and Carath233;odory problems -- 4.4 Neharis problem in two variables -- 4.5 Nehari and Carath233;odory problems for functions on compact groups -- 4.6 The Nevanlinna-Pick problem -- 4.7 The operator Corona problem -- 4.8 Joint operator/Hilbert-Schmidt norm control extensions -- 4.9 An L[sup()] extension problem for polynomials -- 4.10 Superoptimal completions -- 4.11 Superoptimal approximations of analytic functions -- 4.12 Model matching -- 4.13 Exercises -- 4.14 Notes -- Chapter 5. Hermitian and related completion problems -- 5.1 Hermitian completions -- 5.2 Ranks of completions -- 5.3 Minimal negative and positive signature -- 5.4 Inertia of Hermitian matrix expressions -- 5.5 Bounds for eigenvalues of Hermitian completions -- 5.6 Bounds for singular values of completions of partial triangular matrices -- 5.7 Moment problems for real measures on the unit circle -- 5.8 Euclidean distance matrix completions -- 5.9 Normal completions -- 5.10 Application to minimal representation of discrete systems -- 5.11 The separability problem in quantum information -- 5.12 Exercises -- 5.13 Notes -- Bibliography -- Subject Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Notation Index
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{'f': 'http://opac.lib.rpi.edu/record=b4326523'}
Extent
1 online resource (xii, 518 pages)
File format
unknown
Form of item
online
Isbn
9781400840595
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote

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