Linear Algebra Concepts And Methods

Author: Martin Anthony
Editor: Cambridge University Press
ISBN: 0521279488
Size: 18,24 MB
Format: PDF, ePub
Read: 646

Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.

Linear Algebra

Author: Martin Anthony. Michele Harvey
ISBN: 9781107484535
Size: 13,44 MB
Format: PDF, Kindle
Read: 706

This thorough, yet concise, treatment of all the key topics also gives students a sound understanding of the underlying theory.

Linear Algebra And Its Applications

Author: Gilbert Strang
Editor: Academic Press
ISBN: 1483265110
Size: 20,29 MB
Format: PDF
Read: 248

Linear Algebra and Its Applications, Second Edition fulfills the need for a book that will permit the teaching of the applications of linear algebra, in combination with the underlying mathematics. Comprised of eight chapters, the book aims to provide a comprehensive presentation of the concepts and methods in linear algebra. The text starts with the discussion of the Gaussian elimination, the simplest and most useful method of solution. This chapter is followed by chapters that focus on the study of vector spaces, projections and inner products, determinants, and eigenvalues. Discussions on positive definite matrices, computations with matrices, and introduction to linear programming and game theory are provided as well. This text is intended for use by college students.

Matrix Algebra For Linear Models

Author: Marvin H. J. Gruber
Editor: John Wiley & Sons
ISBN: 111860881X
Size: 11,47 MB
Format: PDF, ePub, Docs
Read: 871

A self-contained introduction to matrix analysis theory andapplications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Modelsoffers a succinct summary of matrix theory and its relatedapplications to statistics, especially linear models. The bookprovides a unified presentation of the mathematical properties andstatistical applications of matrices in order to define andmanipulate data. Written for theoretical and applied statisticians, the bookutilizes multiple numerical examples to illustrate key ideas,methods, and techniques crucial to understanding matrixalgebra’s application in linear models. Matrix Algebra forLinear Models expertly balances concepts and methods allowingfor a side-by-side presentation of matrix theory and its linearmodel applications. Including concise summaries on each topic, thebook also features: Methods of deriving results from the properties of eigenvaluesand the singular value decomposition Solutions to matrix optimization problems for obtaining moreefficient biased estimators for parameters in linear regressionmodels A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhanceunderstanding of the presented material Matrix Algebra for Linear Models is an ideal textbook foradvanced undergraduate and graduate-level courses on statistics,matrices, and linear algebra. The book is also an excellentreference for statisticians, engineers, economists, and readersinterested in the linear statistical model.

Advanced Linear Algebra For Engineers With Matlab

Author: Sohail A. Dianat
Editor: CRC Press
ISBN: 1420095242
Size: 18,24 MB
Format: PDF
Read: 804

Arming readers with both theoretical and practical knowledge, Advanced Linear Algebra for Engineers with MATLAB® provides real-life problems that readers can use to model and solve engineering and scientific problems in fields ranging from signal processing and communications to electromagnetics and social and health sciences. Facilitating a unique understanding of rapidly evolving linear algebra and matrix methods, this book: Outlines the basic concepts and definitions behind matrices, matrix algebra, elementary matrix operations, and matrix partitions, describing their potential use in signal and image processing applications Introduces concepts of determinants, inverses, and their use in solving linear equations that result from electrical and mechanical-type systems Presents special matrices, linear vector spaces, and fundamental principles of orthogonality, using an appropriate blend of abstract and concrete examples and then discussing associated applications to enhance readers’ visualization of presented concepts Discusses linear operators, eigenvalues, and eigenvectors, and explores their use in matrix diagonalization and singular value decomposition Extends presented concepts to define matrix polynomials and compute functions using several well-known methods, such as Sylvester’s expansion and Cayley-Hamilton Introduces state space analysis and modeling techniques for discrete and continuous linear systems, and explores applications in control and electromechanical systems, to provide a complete solution for the state space equation Shows readers how to solve engineering problems using least square, weighted least square, and total least square techniques Offers a rich selection of exercises and MATLAB® assignments that build a platform to enhance readers’ understanding of the material Striking the appropriate balance between theory and real-life applications, this book provides both advanced students and professionals in the field with a valuable reference that they will continually consult.

Linear Algebra With Applications

Author: Gareth Williams
Editor: Jones & Bartlett Publishers
ISBN: 1449679544
Size: 13,80 MB
Format: PDF
Read: 761

Updated and revised to increase clarity and further improve student learning, the Eighth Edition of Gareth Williams' classic text is designed for the introductory course in linear algebra. It provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. It is organized into three parts that contain core and optional sections. There is then ample time for the instructor to select the material that gives the course the desired flavor. Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of Rn, matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, developing the rank/nullity theorem, and introducing spaces of matrices and functions. Part 3 completes the course with important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition. Throughout the text the author takes care to fully and clearly develop the mathematical concepts and provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. New exercises can be found throughout that tie back to the modern examples in the text. Key Features of the Eighth Edition: • Updated and revised throughout with new section material and exercises. • Each section begins with a motivating introduction, which ties material to the previously learned topics. • Carefully explained examples illustrate key concepts throughout the text. • Includes such new topics such as QR Factorization and Singular Value Decomposition. • Includes new applications such as a Leslie Matrix model that is used to predict birth and death patterns of animals. • Includes discussions of the role of linear algebra in many areas, such as the operation of the search engine Google and the global structure of the worldwide air transportation network. • A MATLAB manual that ties into the regular course material is included as an appendix. These ideas can be implemented on any matrix algebra software package. This manual consists of 28 sections that tie into the regular course material. • Graphing Calculator Manual included as an appendix. • A Student Solutions Manual that contains solutions to selected exercises is available as a supplement. An Instructors Complete Solutions Manual, test bank, and PowerPoint Lecture Outlines are also available. • Available with WebAssign Online Homework & Assessment

Differential Equations And Linear Algebra

Author: Charles Henry Edwards
Editor: Prentice Hall
ISBN: 9780136054252
Size: 15,67 MB
Format: PDF, ePub, Mobi
Read: 323

Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this book discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. First-Order Differential Equations; Mathematical Models and Numerical Methods; Linear Systems and Matrices; Vector Spaces; Higher-Order Linear Differential Equations; Eigenvalues and Eigenvectors; Linear Systems of Differential Equations; Matrix Exponential Methods; Nonlinear Systems and Phenomena; Laplace Transform Methods; Power Series Methods. For future math majors, engineers, or scientists that have taken two or three semesters of Calculus.

Mathematics For Physicists

Author: Alexander Altland
Editor: Cambridge University Press
ISBN: 1108471226
Size: 11,11 MB
Format: PDF
Read: 413

Introduces fundamental concepts and computational methods of mathematics from the perspective of physicists.

Linear Algebra

Author: M. Thamban Nair
Editor: Springer
ISBN: 9811309264
Size: 13,36 MB
Format: PDF, Kindle
Read: 377

This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications. Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to the end of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.

Handbook Of Linear Algebra

Author: Leslie Hogben
Editor: CRC Press
ISBN: 1420010573
Size: 10,10 MB
Format: PDF, ePub, Docs
Read: 242

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessible layout of parts, chapters, and sections, with each section containing definition, fact, and example segments. The five main parts of the book encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, applications of linear algebra to various mathematical and nonmathematical disciplines, and software packages for linear algebra computations. Within each section, the facts (or theorems) are presented in a list format and include references for each fact to encourage further reading, while the examples illustrate both the definitions and the facts. Linearization often enables difficult problems to be estimated by more manageable linear ones, making the Handbook of Linear Algebra essential reading for professionals who deal with an assortment of mathematical problems.