An Introduction To Applied Matrix Analysis

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An Introduction To Applied Matrix Analysis

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Author : Xiao Qing Jin
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-05-30

An Introduction To Applied Matrix Analysis written by Xiao Qing Jin and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-30 with Mathematics categories.

It is well known that most problems in science and engineering eventually progress into matrix problems. This book gives an elementary introduction to applied matrix theory and it also includes some new results obtained in recent years.The book consists of eight chapters. It includes perturbation and error analysis; the conjugate gradient method for solving linear systems; preconditioning techniques; and least squares algorithms based on orthogonal transformations, etc. The last two chapters include some latest development in the area. In Chap. 7, we construct optimal preconditioners for functions of matrices. More precisely, let f be a function of matrices. Given a matrix A, there are two choices of constructing optimal preconditioners for f(A). Properties of these preconditioners are studied for different functions. In Chap. 8, we study the Bottcher-Wenzel conjecture and discuss related problems.This is a textbook for senior undergraduate or junior graduate students majoring in science and engineering. The material is accessible to students who, in various disciplines, have basic linear algebra, calculus, numerical analysis, and computing knowledge. The book is also useful to researchers in computational science who are interested in applied matrix theory.

Introduction To Applied Linear Algebra

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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07

Introduction To Applied Linear Algebra written by Stephen Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Business & Economics categories.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Introduction To Matrix Analysis And Applications

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Author : Fumio Hiai
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-06

Introduction To Matrix Analysis And Applications written by Fumio Hiai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-06 with Mathematics categories.

Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.

Computational Matrix Analysis

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Author : Alan J. Laub
language : en
Publisher: SIAM
Release Date : 2012-05-10

Computational Matrix Analysis written by Alan J. Laub and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-10 with Mathematics categories.

This text provides an introduction to numerical linear algebra together with its application to solving problems arising in state-space control and systems theory. The book provides a number of elements designed to help the reader learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis and an introduction to finite (IEEE) arithmetic, alongside discussion of mathematical software topics. In addition to the fundamental concepts, the text covers statistical condition estimation and gives an overview of certain computational problems in control and systems theory. Engineers and scientists will find this text valuable as a theoretical resource to complement their work in algorithms. For graduate students beginning their study, or advanced undergraduates, this text is ideal as a one-semester course in numerical linear algebra and is a natural follow-on to the author's previous book, Matrix Analysis for Scientists and Engineers.

Applied Linear Algebra And Matrix Analysis

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Author : Thomas S. Shores
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-14

Applied Linear Algebra And Matrix Analysis written by Thomas S. Shores and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-14 with Mathematics categories.

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.

Matrix Theory

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Author : Robert Piziak
language : en
Publisher: CRC Press
Release Date : 2007-02-22

Matrix Theory written by Robert Piziak and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-22 with Mathematics categories.

In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.

Linear Algebra And Matrix Analysis For Statistics

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Author : Sudipto Banerjee
language : en
Publisher: CRC Press
Release Date : 2014-06-06

Linear Algebra And Matrix Analysis For Statistics written by Sudipto Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-06 with Mathematics categories.

Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Applied Matrix And Tensor Analysis

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Author : John A. Eisele
language : en
Publisher: John Wiley & Sons
Release Date : 1970

Applied Matrix And Tensor Analysis written by John A. Eisele and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

Numerical Matrix Analysis

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Author : Ilse C. F. Ipsen
language : en
Publisher: SIAM
Release Date : 2009-07-23

Numerical Matrix Analysis written by Ilse C. F. Ipsen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-23 with Mathematics categories.

Matrix analysis presented in the context of numerical computation at a basic level.

An Introduction To Applied Multivariate Analysis

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Author : Tenko Raykov
language : en
Publisher: Routledge
Release Date : 2008-03-10

An Introduction To Applied Multivariate Analysis written by Tenko Raykov and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-10 with Business & Economics categories.

This comprehensive text introduces readers to the most commonly used multivariate techniques at an introductory, non-technical level. By focusing on the fundamentals, readers are better prepared for more advanced applied pursuits, particularly on topics that are most critical to the behavioral, social, and educational sciences. Analogies betwe