A01=Rajendra Bhatia
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Binomial theorem
Block matrix
Calculation
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Cauchy matrix
Cauchy-Schwarz inequality
Coefficient
Commutative property
Completely positive map
Complex number
Convex function
Convex set
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Density matrix
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Fourier transform
Gamma function
Geometric mean
Geometry
Hadamard product (matrices)
Harmonic analysis
Hermitian matrix
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Hyperbolic function
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Invertible matrix
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Linear map
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Mathematics
Matrix (mathematics)
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Monotonic function
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Operator algebra
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Orthonormal basis
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Positive element
Positive map
Positive semidefinite
Positive-definite function
Positive-definite matrix
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Product details
- ISBN 9780691168258
- Weight: 369g
- Dimensions: 152 x 235mm
- Publication Date: 01 Sep 2015
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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.
Rajendra Bhatia is Professor of Mathematics at the Indian Statistical Institute in New Delhi. He is the author of five books, including Matrix Analysis.
