00976cam a22002534a 450099100095843970753620080519141822.0101119s2005 it ab b 000 0dita 8855528483b13938034-39ule_instDip.to Studi Storiciita711Categorie geografiche e problematiche di organizzazione territoriale :scritti in onore di Ricciarda SimoncelliBologna :Patron,[2005]469 p. ;24 cm.Simoncelli, RicciardaPianificazione territorialeSimoncelli, Ricciarda .b1393803428-01-1419-11-10991000958439707536LE023 711 PIA 1 1 12023000121931le023-E38.00-l- 00000.i1520002419-11-10Categorie geografiche e problematiche di organizzazione territoriale249867UNISALENTOle02319-11-10ma -itait 0007227nam 22018734a 450 991077772730332120200520144314.01-282-12974-097866121297421-4008-2778-710.1515/9781400827787(CKB)1000000000756263(EBL)445446(OCoLC)330822909(SSID)ssj0000224738(PQKBManifestationID)11910947(PQKBTitleCode)TC0000224738(PQKBWorkID)10210617(PQKB)10076542(DE-B1597)446708(OCoLC)979745018(OCoLC)990529004(DE-B1597)9781400827787(Au-PeEL)EBL445446(CaPaEBR)ebr10284074(CaONFJC)MIL212974(MiAaPQ)EBC445446(PPN)153447087(EXLCZ)99100000000075626320060714d2007 uy 0engur|n|---|||||txtccrPositive definite matrices[electronic resource] /Rajendra BhatiaCourse BookPrinceton, N.J. Princeton University Pressc20071 online resource (265 p.)Princeton series in applied mathematicsDescription based upon print version of record.0-691-16825-3 0-691-12918-5 Includes bibliographical references (p. [237]-245) and index. 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 -- NotationThis 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.Princeton series in applied mathematics.MatricesAddition.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).Matrices.512.9/434SK 220rvkBhatia Rajendra1952-59869MiAaPQMiAaPQMiAaPQBOOK9910777727303321Positive definite matrices1226929UNINA