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100   $a20060714d2007      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aPositive definite matrices$b[electronic resource] /$fRajendra Bhatia
205   $aCourse Book
210   $aPrinceton, N.J. $cPrinceton University Press$dc2007
215   $a1 online resource (265 p.)
225 1 $aPrinceton series in applied mathematics
300   $aDescription based upon print version of record.
311   $a0-691-16825-3 
311   $a0-691-12918-5 
320   $aIncludes bibliographical references (p. [237]-245) and index.
327   $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Positive Matrices -- $tChapter Two. Positive Linear Maps -- $tChapter Three. Completely Positive Maps -- $tChapter Four. Matrix Means -- $tChapter Five. Positive Definite Functions -- $tChapter Six. Geometry of Positive Matrices -- $tBibliography -- $tIndex -- $tNotation
330   $aThis book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.
410  0$aPrinceton series in applied mathematics.
606   $aMatrices
610   $aAddition.
610   $aAnalytic continuation.
610   $aArithmetic mean.
610   $aBanach space.
610   $aBinomial theorem.
610   $aBlock matrix.
610   $aBochner's theorem.
610   $aCalculation.
610   $aCauchy matrix.
610   $aCauchy?Schwarz inequality.
610   $aCharacteristic polynomial.
610   $aCoefficient.
610   $aCommutative property.
610   $aCompact space.
610   $aCompletely positive map.
610   $aComplex number.
610   $aComputation.
610   $aContinuous function.
610   $aConvex combination.
610   $aConvex function.
610   $aConvex set.
610   $aCorollary.
610   $aDensity matrix.
610   $aDiagonal matrix.
610   $aDifferential geometry.
610   $aEigenvalues and eigenvectors.
610   $aEquation.
610   $aEquivalence relation.
610   $aExistential quantification.
610   $aExtreme point.
610   $aFourier transform.
610   $aFunctional analysis.
610   $aFundamental theorem.
610   $aG. H. Hardy.
610   $aGamma function.
610   $aGeometric mean.
610   $aGeometry.
610   $aHadamard product (matrices).
610   $aHahn?Banach theorem.
610   $aHarmonic analysis.
610   $aHermitian matrix.
610   $aHilbert space.
610   $aHyperbolic function.
610   $aInfimum and supremum.
610   $aInfinite divisibility (probability).
610   $aInvertible matrix.
610   $aLecture.
610   $aLinear algebra.
610   $aLinear map.
610   $aLogarithm.
610   $aLogarithmic mean.
610   $aMathematics.
610   $aMatrix (mathematics).
610   $aMatrix analysis.
610   $aMatrix unit.
610   $aMetric space.
610   $aMonotonic function.
610   $aNatural number.
610   $aOpen set.
610   $aOperator algebra.
610   $aOperator system.
610   $aOrthonormal basis.
610   $aPartial trace.
610   $aPositive definiteness.
610   $aPositive element.
610   $aPositive map.
610   $aPositive semidefinite.
610   $aPositive-definite function.
610   $aPositive-definite matrix.
610   $aProbability measure.
610   $aProbability.
610   $aProjection (linear algebra).
610   $aQuantity.
610   $aQuantum computing.
610   $aQuantum information.
610   $aQuantum statistical mechanics.
610   $aReal number.
610   $aRiccati equation.
610   $aRiemannian geometry.
610   $aRiemannian manifold.
610   $aRiesz representation theorem.
610   $aRight half-plane.
610   $aSchur complement.
610   $aSchur's theorem.
610   $aScientific notation.
610   $aSelf-adjoint operator.
610   $aSign (mathematics).
610   $aSpecial case.
610   $aSpectral theorem.
610   $aSquare root.
610   $aStandard basis.
610   $aSummation.
610   $aTensor product.
610   $aTheorem.
610   $aToeplitz matrix.
610   $aUnit vector.
610   $aUnitary matrix.
610   $aUnitary operator.
610   $aUpper half-plane.
610   $aVariable (mathematics).
615  0$aMatrices.
676   $a512.9/434
686   $aSK 220$2rvk
700   $aBhatia$b Rajendra$f1952-$059869
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910777727303321
996   $aPositive definite matrices$91226929
997   $aUNINA