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Positive Definite Matrices
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Book Synopsis Positive Definite Matrices by : Rajendra Bhatia
Download or read book Positive Definite Matrices written by Rajendra Bhatia and published by Princeton University Press. This book was released on 2015-09-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Positive Definite Matrices by : Rajendra Bhatia
Download or read book Positive Definite Matrices written by Rajendra Bhatia and published by Princeton University Press. This book was released on 2009-01-10 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Positive Definite Matrices by : Rajendra Bhatia
Download or read book Positive Definite Matrices written by Rajendra Bhatia and published by Princeton University Press. This book was released on 2007-01-07 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Matrix Analysis by : Rajendra Bhatia
Download or read book Matrix Analysis written by Rajendra Bhatia and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.
Book Synopsis Visualization and Processing of Tensor Fields by : Joachim Weickert
Download or read book Visualization and Processing of Tensor Fields written by Joachim Weickert and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix-valued data sets – so-called second order tensor fields – have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.
Book Synopsis Differential Equations and Linear Algebra by : Gilbert Strang
Download or read book Differential Equations and Linear Algebra written by Gilbert Strang and published by Wellesley-Cambridge Press. This book was released on 2015-02-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Book Synopsis Numerical Linear Algebra and Matrix Factorizations by : Tom Lyche
Download or read book Numerical Linear Algebra and Matrix Factorizations written by Tom Lyche and published by Springer Nature. This book was released on 2020-03-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Book Synopsis Matrix Positivity by : Charles R. Johnson
Download or read book Matrix Positivity written by Charles R. Johnson and published by Cambridge University Press. This book was released on 2020-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.
Download or read book Ants XIV written by Steven Galbraith and published by . This book was released on 2020-12-29 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Algorithmic Number Theory Symposium (ANTS), held biennially since 1994, is the premier international forum for research in computational and algorithmic number theory. ANTS is devoted to algorithmic aspects of number theory, including elementary, algebraic, and analytic number theory, the geometry of numbers, arithmetic algebraic geometry, the theory of finite fields, and cryptography.This volume is the proceedings of the fourteenth ANTS meeting, which took place 29 June to 4 July 2020 via video conference, the plans for holding it at the University of Auckland, New Zealand, having been disrupted by the COVID-19 pandemic. The volume contains revised and edited versions of 24 refereed papers and one invited paper presented at the conference.
Book Synopsis Geodesy - the Challenge of the 3rd Millennium by : Erik Grafarend
Download or read book Geodesy - the Challenge of the 3rd Millennium written by Erik Grafarend and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geodesy as the science which determines the figure of the earth, its orientation in space and its gravity field as well as its temporal changes, produces key elements in describing the kinematics and the dynamics of the deformable body "earth". It contributes in particular to geodynamics and opens the door to decode the complex interactions between components of "the system earth". In the breathtaking development recently a whole arsenal of new terrestrial, airborne as well as satelliteborne measurement techniques for earth sciences have been made available and have broadened the spectrum of measurable earth parameters with an unforeseen accuracy and precision, in particular to resolve the factor time. The book focusses on these topics and gives a state of the art of modern geodesy.
Book Synopsis A Mathematical Primer for Social Statistics by : John Fox
Download or read book A Mathematical Primer for Social Statistics written by John Fox and published by SAGE Publications. This book was released on 2021-01-11 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Primer for Social Statistics, Second Edition presents mathematics central to learning and understanding statistical methods beyond the introductory level: the basic "language" of matrices and linear algebra and its visual representation, vector geometry; differential and integral calculus; probability theory; common probability distributions; statistical estimation and inference, including likelihood-based and Bayesian methods. The volume concludes by applying mathematical concepts and operations to a familiar case, linear least-squares regression. The Second Edition pays more attention to visualization, including the elliptical geometry of quadratic forms and its application to statistics. It also covers some new topics, such as an introduction to Markov-Chain Monte Carlo methods, which are important in modern Bayesian statistics. A companion website includes materials that enable readers to use the R statistical computing environment to reproduce and explore computations and visualizations presented in the text. The book is an excellent companion to a "math camp" or a course designed to provide foundational mathematics needed to understand relatively advanced statistical methods.
Book Synopsis Nonnegative Matrices and Applications by : R. B. Bapat
Download or read book Nonnegative Matrices and Applications written by R. B. Bapat and published by Cambridge University Press. This book was released on 1997-03-28 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Book Synopsis Completely Positive Matrices by : Abraham Berman
Download or read book Completely Positive Matrices written by Abraham Berman and published by World Scientific. This book was released on 2003 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A = BBOC is known as the cp- rank of A . This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp- rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The CP Completion Problem; CP Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."
Book Synopsis Computer Vision – ECCV 2012 by : Andrew Fitzgibbon
Download or read book Computer Vision – ECCV 2012 written by Andrew Fitzgibbon and published by Springer. This book was released on 2012-09-26 with total page 909 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seven-volume set comprising LNCS volumes 7572-7578 constitutes the refereed proceedings of the 12th European Conference on Computer Vision, ECCV 2012, held in Florence, Italy, in October 2012. The 408 revised papers presented were carefully reviewed and selected from 1437 submissions. The papers are organized in topical sections on geometry, 2D and 3D shapes, 3D reconstruction, visual recognition and classification, visual features and image matching, visual monitoring: action and activities, models, optimisation, learning, visual tracking and image registration, photometry: lighting and colour, and image segmentation.
Book Synopsis The Schur Complement and Its Applications by : Fuzhen Zhang
Download or read book The Schur Complement and Its Applications written by Fuzhen Zhang and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. Coverage includes historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis.
Book Synopsis Interior-point Polynomial Algorithms in Convex Programming by : Yurii Nesterov
Download or read book Interior-point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.
