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Positive definite matrices [[electronic resource] /] / Rajendra Bhatia



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Autore: Bhatia Rajendra <1952-> Visualizza persona
Titolo: Positive definite matrices [[electronic resource] /] / Rajendra Bhatia Visualizza cluster
Pubblicazione: Princeton, N.J., : Princeton University Press, c2007
Edizione: Course Book
Descrizione fisica: 1 online resource (265 p.)
Disciplina: 512.9/434
Soggetto topico: Matrices
Soggetto non controllato: Addition
Analytic continuation
Arithmetic mean
Banach space
Binomial theorem
Block matrix
Bochner's theorem
Calculation
Cauchy matrix
Cauchy–Schwarz inequality
Characteristic polynomial
Coefficient
Commutative property
Compact space
Completely positive map
Complex number
Computation
Continuous function
Convex combination
Convex function
Convex set
Corollary
Density matrix
Diagonal matrix
Differential geometry
Eigenvalues and eigenvectors
Equation
Equivalence relation
Existential quantification
Extreme point
Fourier transform
Functional analysis
Fundamental theorem
G. H. Hardy
Gamma function
Geometric mean
Geometry
Hadamard product (matrices)
Hahn–Banach theorem
Harmonic analysis
Hermitian matrix
Hilbert space
Hyperbolic function
Infimum and supremum
Infinite divisibility (probability)
Invertible matrix
Lecture
Linear algebra
Linear map
Logarithm
Logarithmic mean
Mathematics
Matrix (mathematics)
Matrix analysis
Matrix unit
Metric space
Monotonic function
Natural number
Open set
Operator algebra
Operator system
Orthonormal basis
Partial trace
Positive definiteness
Positive element
Positive map
Positive semidefinite
Positive-definite function
Positive-definite matrix
Probability measure
Probability
Projection (linear algebra)
Quantity
Quantum computing
Quantum information
Quantum statistical mechanics
Real number
Riccati equation
Riemannian geometry
Riemannian manifold
Riesz representation theorem
Right half-plane
Schur complement
Schur's theorem
Scientific notation
Self-adjoint operator
Sign (mathematics)
Special case
Spectral theorem
Square root
Standard basis
Summation
Tensor product
Theorem
Toeplitz matrix
Unit vector
Unitary matrix
Unitary operator
Upper half-plane
Variable (mathematics)
Classificazione: SK 220
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references (p. [237]-245) and index.
Nota di contenuto: Frontmatter -- Contents -- Preface -- Chapter One. Positive Matrices -- Chapter Two. Positive Linear Maps -- Chapter Three. Completely Positive Maps -- Chapter Four. Matrix Means -- Chapter Five. Positive Definite Functions -- Chapter Six. Geometry of Positive Matrices -- Bibliography -- Index -- Notation
Sommario/riassunto: This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.
Titolo autorizzato: Positive definite matrices  Visualizza cluster
ISBN: 1-282-12974-0
9786612129742
1-4008-2778-7
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910777727303321
Lo trovi qui: Univ. Federico II
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Serie: Princeton series in applied mathematics.