Basic Matrix Algebra With Algorithms And Applications

Author : Robert A. Liebler
Publisher : CRC Press
Page : 260 pages
File Size : 44,7 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9780429852879

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Basic Matrix Algebra with Algorithms and Applications by Robert A. Liebler Pdf

Clear prose, tight organization, and a wealth of examples and computational techniques make Basic Matrix Algebra with Algorithms and Applications an outstanding introduction to linear algebra. The author designed this treatment specifically for freshman majors in mathematical subjects and upper-level students in natural resources, the social sciences, business, or any discipline that eventually requires an understanding of linear models. With extreme pedagogical clarity that avoids abstraction wherever possible, the author emphasizes minimal polynomials and their computation using a Krylov algorithm. The presentation is highly visual and relies heavily on work with a graphing calculator to allow readers to focus on concepts and techniques rather than on tedious arithmetic. Supporting materials, including test preparation Maple worksheets, are available for download from the Internet. This unassuming but insightful and remarkably original treatment is organized into bite-sized, clearly stated objectives. It goes well beyond the LACSG recommendations for a first course while still implementing their philosophy and core material. Classroom tested with great success, it prepares readers well for the more advanced studies their fields ultimately will require.

Author : James E. Gentle
Publisher : Springer Nature
Page : 714 pages
File Size : 48,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9783031421440

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Matrix Algebra by James E. Gentle Pdf

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 46,5 Mb
Release : 2007-07-27
Category : Computers
ISBN : 9780387708720

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Matrix Algebra by James E. Gentle Pdf

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Author : Larisa Beilina,Evgenii Karchevskii,Mikhail Karchevskii
Publisher : Springer
Page : 450 pages
File Size : 55,6 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9783319573045

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Numerical Linear Algebra: Theory and Applications by Larisa Beilina,Evgenii Karchevskii,Mikhail Karchevskii Pdf

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789814469555

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Matrix Methods: Theory, Algorithms and Applications by Anonim Pdf

Author : G. W. Stewart
Publisher : SIAM
Page : 476 pages
File Size : 44,5 Mb
Release : 1998-08-01
Category : Mathematics
ISBN : 9780898714142

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Matrix Algorithms by G. W. Stewart Pdf

This volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.

Author : Edward Barry Saff,Arthur David Snider
Publisher : John Wiley & Sons
Page : 407 pages
File Size : 41,6 Mb
Release : 2015-10-12
Category : Mathematics
ISBN : 9781118953655

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Fundamentals of Matrix Analysis with Applications by Edward Barry Saff,Arthur David Snider Pdf

An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.

Author : Dario Andrea Bini,Fabio Di Benedetto,Eugene Tyrtyshnikov,Marc Van Barel
Publisher : Springer
Page : 322 pages
File Size : 44,5 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9783030040888

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Structured Matrices in Numerical Linear Algebra by Dario Andrea Bini,Fabio Di Benedetto,Eugene Tyrtyshnikov,Marc Van Barel Pdf

This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.

Author : Richard Bronson,Gabriel B. Costa,John T. Saccoman,Daniel Gross
Publisher : Elsevier
Page : 530 pages
File Size : 54,9 Mb
Release : 2023-02-27
Category : Mathematics
ISBN : 9780323984270

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Linear Algebra by Richard Bronson,Gabriel B. Costa,John T. Saccoman,Daniel Gross Pdf

Linear Algebra: Algorithms, Applications, and Techniques, Fourth Edition offers a modern and algorithmic approach to computation while providing clear and straightforward theoretical background information. The book guides readers through the major applications, with chapters on properties of real numbers, proof techniques, matrices, vector spaces, linear transformations, eigen values, and Euclidean inner products. Appendices on Jordan canonical forms and Markov chains are included for further study. This useful textbook presents broad and balanced views of theory, with key material highlighted and summarized in each chapter. To further support student practice, the book also includes ample exercises with answers and hints. Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs Provides a balanced approach to computation and theory by offering computational algorithms for finding eigenvalues and eigenvectors Offers excellent exercise sets, ranging from drill to theoretical/challenging, along with useful and interesting applications not found in other introductory linear algebra texts

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206231

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Numerical Linear Algebra for Applications in Statistics by James E. Gentle Pdf

Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.

Author : Richard Bronson,Gabriel B. Costa,John T. Saccoman
Publisher : Academic Press
Page : 532 pages
File Size : 53,7 Mb
Release : 2013-10-08
Category : Mathematics
ISBN : 9780123978110

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Linear Algebra by Richard Bronson,Gabriel B. Costa,John T. Saccoman Pdf

In this appealing and well-written text, Richard Bronson starts with the concrete and computational, and leads the reader to a choice of major applications. The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced and key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. Prerequisite: One year of calculus is recommended. Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs Provides a balanced approach to computation and theory by offering computational algorithms for finding eigenvalues and eigenvectors Offers excellent exercise sets, ranging from drill to theoretical/challeging along with useful and interesting applications not found in other introductory linear algebra texts

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 51,8 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

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

Author : Philip N. Klein
Publisher : Unknown
Page : 530 pages
File Size : 52,8 Mb
Release : 2013-07
Category : Algebras, Linear
ISBN : 061585673X

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Coding the Matrix by Philip N. Klein Pdf

An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.

Author : Darald J. Hartfiel
Publisher : CRC Press
Page : 382 pages
File Size : 44,8 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9781482285635

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Matrix Theory and Applications with MATLAB by Darald J. Hartfiel Pdf

Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text. All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology. Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own.

Author : Gene H. Golub,Gérard Meurant
Publisher : Princeton University Press
Page : 376 pages
File Size : 40,9 Mb
Release : 2009-12-07
Category : Mathematics
ISBN : 9781400833887

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Matrices, Moments and Quadrature with Applications by Gene H. Golub,Gérard Meurant Pdf

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.