Positive Definite Matrices

Author : Rajendra Bhatia
Publisher : Princeton University Press
Page : 264 pages
File Size : 41,7 Mb
Release : 2015-09-01
Category : Mathematics
ISBN : 9780691168258

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Positive Definite Matrices by Rajendra Bhatia Pdf

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.

Author : Rajendra Bhatia
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 52,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461206538

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Matrix Analysis by Rajendra Bhatia Pdf

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.

Author : Daniel Zelinsky
Publisher : Academic Press
Page : 276 pages
File Size : 53,6 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483265001

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A First Course in Linear Algebra by Daniel Zelinsky Pdf

A First Course in Linear Algebra provides an introduction to the algebra and geometry of vectors, matrices, and linear transformations. This book is designed as a background for second-year courses in calculus of several variables and differential equations where the theory of linear differential equations parallels that of linear algebraic equations. The topics discussed include the multiplication of vectors by scalars, vectors in n-space, planes and lines, and composites of linear mappings. The symmetric matrices and mappings, quadratic forms, change of coordinates, and effect of change of basis on matrices of linear functions are also described. This text likewise considers the computation of determinants, diagonalizable transformations, computation of eigenvalues and eigenvectors, and principal axis theorem. This publication is suitable for college students taking a course in linear algebra.

Author : Joachim Weickert,Hans Hagen
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 44,6 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9783540312727

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Visualization and Processing of Tensor Fields by Joachim Weickert,Hans Hagen Pdf

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.

Author : Abraham Berman,Naomi Shaked-Monderer
Publisher : World Scientific
Page : 222 pages
File Size : 49,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9812795219

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Completely Positive Matrices by Abraham Berman,Naomi Shaked-Monderer Pdf

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."

Author : Rajendra Bhatia
Publisher : Unknown
Page : 254 pages
File Size : 55,8 Mb
Release : 1996
Category : Electronic
ISBN : OCLC:817079457

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Positive Definite Matrices by Rajendra Bhatia Pdf

Author : Edwin F. Beckenbach,R. Bellman
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642649714

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Inequalities by Edwin F. Beckenbach,R. Bellman Pdf

Since the elassie work on inequalities by HARDY, LITTLEWOOD, and P6LYA in 1934, an enonnous amount of effort has been devoted to the sharpening and extension of the elassieal inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us eite the fields of ordinary and partial differential equations, whieh are dominated by inequalities and variational prineiples involving functions and their derivatives; the many applications of linear inequalities to game theory and mathe matieal economics, which have triggered a renewed interest in con vexity and moment-space theory; and the growing uses of digital com puters, which have given impetus to a systematie study of error esti mates involving much sophisticated matrix theory and operator theory. The results presented in the following pages reflect to some extent these ramifications of inequalities into contiguous regions of analysis, but to a greater extent our concem is with inequalities in their native habitat. Since it is elearly impossible to give a connected account of the burst of analytic activity of the last twenty-five years centering about inequalities, we have d. eeided to limit our attention to those topies that have particularly delighted and intrigued us, and to the study of whieh we have contributed.

Author : Charles R. Johnson,Ronald L. Smith,Michael J. Tsatsomeros
Publisher : Cambridge University Press
Page : 223 pages
File Size : 50,8 Mb
Release : 2020-10
Category : Mathematics
ISBN : 9781108478717

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Matrix Positivity by Charles R. Johnson,Ronald L. Smith,Michael J. Tsatsomeros Pdf

This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.

Author : M. H. Lietzke
Publisher : Unknown
Page : 44 pages
File Size : 42,6 Mb
Release : 1963
Category : Matrices
ISBN : UOM:39015077306945

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A Comparison of Several Methods for Inverting Large Symmetric Positive Definite Matrices by M. H. Lietzke Pdf

Author : Andrew Fitzgibbon,Svetlana Lazebnik,Pietro Perona,Yoichi Sato,Cordelia Schmid
Publisher : Springer
Page : 889 pages
File Size : 52,6 Mb
Release : 2012-09-26
Category : Computers
ISBN : 9783642337093

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Computer Vision – ECCV 2012 by Andrew Fitzgibbon,Svetlana Lazebnik,Pietro Perona,Yoichi Sato,Cordelia Schmid Pdf

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.

Author : Yurii Nesterov,Arkadii Nemirovskii
Publisher : SIAM
Page : 414 pages
File Size : 48,5 Mb
Release : 1994-01-01
Category : Mathematics
ISBN : 1611970792

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Interior-point Polynomial Algorithms in Convex Programming by Yurii Nesterov,Arkadii Nemirovskii Pdf

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.

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 0 pages
File Size : 51,8 Mb
Release : 2015-02-12
Category : Mathematics
ISBN : 0980232791

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Differential Equations and Linear Algebra by Gilbert Strang Pdf

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.

Author : R. B. Bapat,T. E. S. Raghavan
Publisher : Cambridge University Press
Page : 351 pages
File Size : 47,8 Mb
Release : 1997-03-28
Category : Mathematics
ISBN : 9780521571678

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Nonnegative Matrices and Applications by R. B. Bapat,T. E. S. Raghavan Pdf

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.

Author : Tom Lyche
Publisher : Springer Nature
Page : 376 pages
File Size : 52,9 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9783030364687

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Numerical Linear Algebra and Matrix Factorizations by Tom Lyche Pdf

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.

Author : Erik Grafarend,Friedrich W. Krumm,Volker S. Schwarze
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 46,5 Mb
Release : 2013-12-11
Category : Science
ISBN : 9783662052969

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Geodesy - the Challenge of the 3rd Millennium by Erik Grafarend,Friedrich W. Krumm,Volker S. Schwarze Pdf

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.