Matrix completions, moments, and sums of hermitian squares

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

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...

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Bibliographic Details
Main Authors: Bakonyi, M. (Mihály), 1962- (Author), Woerdeman, Hugo J. (Hugo Jan), 1962- (Author)
Format: eBook
Language:English
Published: Princeton : Princeton University Press, ©2011.
Series:Princeton series in applied mathematics.
Subjects:
Algebras, Linear.
Hermitian forms.
Matrices.
MATHEMATICS > Matrices.
Algebras, Linear
Hermitian forms
Matrices
Online Access:Click for online access
Table of 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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