Positive Definite Matrices / / Rajendra Bhatia.
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...
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| 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 ;
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Bhatia, Rajendra, author. aut http://id.loc.gov/vocabulary/relators/aut Positive Definite Matrices / Rajendra Bhatia. Course Book Princeton, NJ : Princeton University Press, [2009] ©2007 1 online resource (240 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Series in Applied Mathematics ; 53 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) MATHEMATICS Geometry Differential. Mathematics Matrices. Matrices. MATHEMATICS / Matrices. bisacsh 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). Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package 9783110515831 ZDB-23-PAM Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691129181 https://doi.org/10.1515/9781400827787 https://www.degruyter.com/isbn/9781400827787 Cover https://www.degruyter.com/document/cover/isbn/9781400827787/original |
| language |
English |
| format |
eBook |
| author |
Bhatia, Rajendra, Bhatia, Rajendra, |
| spellingShingle |
Bhatia, Rajendra, Bhatia, Rajendra, Positive Definite Matrices / Princeton Series in Applied Mathematics ; 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 |
| author_facet |
Bhatia, Rajendra, Bhatia, Rajendra, |
| author_variant |
r b rb r b rb |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
Bhatia, Rajendra, |
| title |
Positive Definite Matrices / |
| title_full |
Positive Definite Matrices / Rajendra Bhatia. |
| title_fullStr |
Positive Definite Matrices / Rajendra Bhatia. |
| title_full_unstemmed |
Positive Definite Matrices / Rajendra Bhatia. |
| title_auth |
Positive Definite Matrices / |
| title_alt |
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 |
| title_new |
Positive Definite Matrices / |
| title_sort |
positive definite matrices / |
| series |
Princeton Series in Applied Mathematics ; |
| series2 |
Princeton Series in Applied Mathematics ; |
| publisher |
Princeton University Press, |
| publishDate |
2009 |
| physical |
1 online resource (240 p.) Issued also in print. |
| edition |
Course Book |
| contents |
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 |
| isbn |
9781400827787 9783110515831 9783110442502 9780691129181 |
| callnumber-first |
Q - Science |
| callnumber-subject |
QA - Mathematics |
| callnumber-label |
QA188 |
| callnumber-sort |
QA 3188 |
| genre_facet |
Geometry Differential. Matrices. |
| url |
https://doi.org/10.1515/9781400827787 https://www.degruyter.com/isbn/9781400827787 https://www.degruyter.com/document/cover/isbn/9781400827787/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
512 - Algebra |
| dewey-full |
512.9/434 |
| dewey-sort |
3512.9 3434 |
| dewey-raw |
512.9/434 |
| dewey-search |
512.9/434 |
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10.1515/9781400827787 |
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979745018 |
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Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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Positive Definite Matrices / |
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Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package |
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