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
 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 selfcontained, 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
 Language
 eng
 Extent
 1 online resource (xii, 518 pages)
 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;rRiesz 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 ChristoffelDarboux formulas
 3.3 Twovariable moment problem for BernsteinSzeg246; measures
 3.4 Fej233;rRiesz 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 Twovariable 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 operatormatrix completions
 4.2 Linearly constrained completion problems
 4.3 The operatorvalued 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 NevanlinnaPick problem
 4.7 The operator Corona problem
 4.8 Joint operator/HilbertSchmidt 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
 Isbn
 9781400840595
 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
 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 selfcontained, 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
 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
 Label
 Matrix completions, moments, and sums of hermitian squares, Mihály Bakonyi and Hugo J. Woerdeman
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 475512) 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;rRiesz 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 ChristoffelDarboux formulas  3.3 Twovariable moment problem for BernsteinSzeg246; measures  3.4 Fej233;rRiesz 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 Twovariable 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 operatormatrix completions  4.2 Linearly constrained completion problems  4.3 The operatorvalued 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 NevanlinnaPick problem  4.7 The operator Corona problem  4.8 Joint operator/HilbertSchmidt 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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