Positive Definite Matrices /

Positive Definite Matrices / / Rajendra Bhatia.

Show other versions (1)

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 d...

Full description

Saved in:
Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package
VerfasserIn:
Bhatia, Rajendra,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2009]
©2007
Year of Publication:2009
Edition:Course Book
Language:English
Series:Princeton Series in Applied Mathematics ; 53
Online Access:
Physical Description:1 online resource (240 p.)
Tags: Add Tag
No Tags, Be the first to tag this record!
LEADER 07999nam a22019575i 4500
001 9781400827787
003 DE-B1597
005 20220131112047.0
006 m|||||o||d||||||||
007 cr || ||||||||
008 220131t20092007nju fo d z eng d
019 |a (OCoLC)990529004 
020 |a 9781400827787 
024 7 |a 10.1515/9781400827787  |2 doi 
035 |a (DE-B1597)446708 
035 |a (OCoLC)979745018 
040 |a DE-B1597  |b eng  |c DE-B1597  |e rda 
041 0 |a eng 
044 |a nju  |c US-NJ 
050 4 |a QA188 
072 7 |a MAT019000  |2 bisacsh 
082 0 4 |a 512.9/434  |2 22 
100 1 |a Bhatia, Rajendra,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Positive Definite Matrices /  |c Rajendra Bhatia. 
250 |a Course Book 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2009] 
264 4 |c ©2007 
300 |a 1 online resource (240 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 0 |a Princeton Series in Applied Mathematics ;  |v 53 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t Chapter One. Positive Matrices --   |t Chapter Two. Positive Linear Maps --   |t Chapter Three. Completely Positive Maps --   |t Chapter Four. Matrix Means --   |t Chapter Five. Positive Definite Functions --   |t Chapter Six. Geometry of Positive Matrices --   |t Bibliography --   |t Index --   |t Notation 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a MATHEMATICS  |v Geometry  |v Differential. 
650 0 |a Mathematics  |v Matrices. 
650 0 |a Matrices. 
650 7 |a MATHEMATICS / Matrices.  |2 bisacsh 
653 |a Addition. 
653 |a Analytic continuation. 
653 |a Arithmetic mean. 
653 |a Banach space. 
653 |a Binomial theorem. 
653 |a Block matrix. 
653 |a Bochner's theorem. 
653 |a Calculation. 
653 |a Cauchy matrix. 
653 |a Cauchy-Schwarz inequality. 
653 |a Characteristic polynomial. 
653 |a Coefficient. 
653 |a Commutative property. 
653 |a Compact space. 
653 |a Completely positive map. 
653 |a Complex number. 
653 |a Computation. 
653 |a Continuous function. 
653 |a Convex combination. 
653 |a Convex function. 
653 |a Convex set. 
653 |a Corollary. 
653 |a Density matrix. 
653 |a Diagonal matrix. 
653 |a Differential geometry. 
653 |a Eigenvalues and eigenvectors. 
653 |a Equation. 
653 |a Equivalence relation. 
653 |a Existential quantification. 
653 |a Extreme point. 
653 |a Fourier transform. 
653 |a Functional analysis. 
653 |a Fundamental theorem. 
653 |a G. H. Hardy. 
653 |a Gamma function. 
653 |a Geometric mean. 
653 |a Geometry. 
653 |a Hadamard product (matrices). 
653 |a Hahn-Banach theorem. 
653 |a Harmonic analysis. 
653 |a Hermitian matrix. 
653 |a Hilbert space. 
653 |a Hyperbolic function. 
653 |a Infimum and supremum. 
653 |a Infinite divisibility (probability). 
653 |a Invertible matrix. 
653 |a Lecture. 
653 |a Linear algebra. 
653 |a Linear map. 
653 |a Logarithm. 
653 |a Logarithmic mean. 
653 |a Mathematics. 
653 |a Matrix (mathematics). 
653 |a Matrix analysis. 
653 |a Matrix unit. 
653 |a Metric space. 
653 |a Monotonic function. 
653 |a Natural number. 
653 |a Open set. 
653 |a Operator algebra. 
653 |a Operator system. 
653 |a Orthonormal basis. 
653 |a Partial trace. 
653 |a Positive definiteness. 
653 |a Positive element. 
653 |a Positive map. 
653 |a Positive semidefinite. 
653 |a Positive-definite function. 
653 |a Positive-definite matrix. 
653 |a Probability measure. 
653 |a Probability. 
653 |a Projection (linear algebra). 
653 |a Quantity. 
653 |a Quantum computing. 
653 |a Quantum information. 
653 |a Quantum statistical mechanics. 
653 |a Real number. 
653 |a Riccati equation. 
653 |a Riemannian geometry. 
653 |a Riemannian manifold. 
653 |a Riesz representation theorem. 
653 |a Right half-plane. 
653 |a Schur complement. 
653 |a Schur's theorem. 
653 |a Scientific notation. 
653 |a Self-adjoint operator. 
653 |a Sign (mathematics). 
653 |a Special case. 
653 |a Spectral theorem. 
653 |a Square root. 
653 |a Standard basis. 
653 |a Summation. 
653 |a Tensor product. 
653 |a Theorem. 
653 |a Toeplitz matrix. 
653 |a Unit vector. 
653 |a Unitary matrix. 
653 |a Unitary operator. 
653 |a Upper half-plane. 
653 |a Variable (mathematics). 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Series in Applied Mathematics eBook-Package  |z 9783110515831  |o ZDB-23-PAM 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Backlist 2000-2013  |z 9783110442502 
776 0 |c print  |z 9780691129181 
856 4 0 |u https://doi.org/10.1515/9781400827787 
856 4 0 |u https://www.degruyter.com/isbn/9781400827787 
856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400827787/original 
912 |a 978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013  |c 2000  |d 2013 
912 |a EBA_BACKALL 
912 |a EBA_CL_MTPY 
912 |a EBA_EBACKALL 
912 |a EBA_EBKALL 
912 |a EBA_ECL_MTPY 
912 |a EBA_EEBKALL 
912 |a EBA_ESTMALL 
912 |a EBA_PPALL 
912 |a EBA_STMALL 
912 |a GBV-deGruyter-alles 
912 |a PDA12STME 
912 |a PDA13ENGE 
912 |a PDA18STMEE 
912 |a PDA5EBK 
912 |a ZDB-23-PAM 

Similar Items