Elementary Matrix Algebra

Elementary Matrix Algebra

PDF Elementary Matrix Algebra Download

  • Author: Franz E. Hohn
  • Publisher: Courier Corporation
  • ISBN: 0486143724
  • Category : Mathematics
  • Languages : en
  • Pages : 562

This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations — homogeneous or nonhomogeneous — and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology. Other subjects include the complete treatment of the structure of the solution space of a system of linear equations, the most commonly used properties of determinants, and linear operators and linear transformations of coordinates. Considerably more material than can be offered in a one-semester course appears here; this comprehensive volume by Franz E. Hohn, Professor of Mathematics at the University of Illinois for many years, provides instructors with a wide range of choices in order to meet differing interests and to accommodate students with varying backgrounds.


Basics of Matrix Algebra for Statistics with R

Basics of Matrix Algebra for Statistics with R

PDF Basics of Matrix Algebra for Statistics with R Download

  • Author: Nick Fieller
  • Publisher: CRC Press
  • ISBN: 1315360055
  • Category : Mathematics
  • Languages : en
  • Pages : 159

A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.


Linear Algebra with Mathematica

Linear Algebra with Mathematica

PDF Linear Algebra with Mathematica Download

  • Author: Fred Szabo
  • Publisher: Academic Press
  • ISBN: 9780126801354
  • Category : Computers
  • Languages : en
  • Pages : 682

Linear Algebra: An Introduction With Mathematica uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and statistics. Includes a thematic presentation of linear algebra Provides a systematic integration of Mathematica Encourages students to appreciate the benefits of mathematical rigor All exercises can be solved with Mathematica


Introduction to linear algebra

Introduction to linear algebra

PDF Introduction to linear algebra Download

  • Author: Gordon Mills
  • Publisher: Transaction Publishers
  • ISBN: 141282656X
  • Category : Mathematics
  • Languages : en
  • Pages : 238

This is the first book on linear algebra written specifically for social scientists. It deals only with those aspects of the subject applicable in the social sciences and provides a thorough understanding of linear algebra for those who wish to use it as a tool in the design, execution, and interpretation of research. Linear mathematical models play an important role in all of the social sciences. This book provides a step-by-step introduction to those parts of linear algebra which are useful in such model building. It illustrates some of the applications of linear analysis and helps the reader learn how to convert his formulation of a social science problem into algebraic terms. The author covers matrix algebra, computational methods, linear models involving discrete variables, and clear, complete explanations of necessary mathematical concepts. Prior knowledge of calculus is not required since no use is made of calculus or of complex numbers. A novel feature of the mathematical content of the book is the treatment of models expressed in terms of variables which must be whole numbers (integers). The book is distinguished by a step-by-step exposition that allows the reader to grasp quickly and fully the principles of linear algebra. All of the examples used to illustrate the text are drawn from the social sciences, enabling the reader to relate the subject to concrete problems in his field. Exercises are included as a necessary part of the text to develop points not covered in the text and to provide practice in the algebraic formulation of applied problems. An appendix gives solutions (or hints) for selected exercises. Gordon Mills is an honorary professor in the department of economics at the University of Sydney. His research interests include transport and retailing, microeconomics, and microeconomic policy especially regulation and privatization. He is the author of many journal articles.


Differential Equations with Linear Algebra

Differential Equations with Linear Algebra

PDF Differential Equations with Linear Algebra Download

  • Author: Matthew R. Boelkins
  • Publisher: Oxford University Press
  • ISBN: 0199736669
  • Category : Mathematics
  • Languages : en
  • Pages : 573

Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, the book is appropriate for courses for majors in mathematics, science, and engineering that study systems of differential equations. Because of its emphasis on linearity, the text opens with a full chapter devoted to essential ideas in linear algebra. Motivated by future problems in systems of differential equations, the chapter on linear algebra introduces such key ideas as systems of algebraic equations, linear combinations, the eigenvalue problem, and bases and dimension of vector spaces. This chapter enables students to quickly learn enough linear algebra to appreciate the structure of solutions to linear differential equations and systems thereof in subsequent study and to apply these ideas regularly. The book offers an example-driven approach, beginning each chapter with one or two motivating problems that are applied in nature. The following chapter develops the mathematics necessary to solve these problems and explores related topics further. Even in more theoretical developments, we use an example-first style to build intuition and understanding before stating or proving general results. Over 100 figures provide visual demonstration of key ideas; the use of the computer algebra system Maple and Microsoft Excel are presented in detail throughout to provide further perspective and support students' use of technology in solving problems. Each chapter closes with several substantial projects for further study, many of which are based in applications. Errata sheet available at: www.oup.com/us/companion.websites/9780195385861/pdf/errata.pdf


A Modern Introduction to Linear Algebra

A Modern Introduction to Linear Algebra

PDF A Modern Introduction to Linear Algebra Download

  • Author: Henry Ricardo
  • Publisher: CRC Press
  • ISBN: 1439894612
  • Category : Mathematics
  • Languages : en
  • Pages : 672

Useful Concepts and Results at the Heart of Linear AlgebraA one- or two-semester course for a wide variety of students at the sophomore/junior undergraduate levelA Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of linear algebra. Concrete, easy-to-understand examples m


Linear Algebra with Applications

Linear Algebra with Applications

PDF Linear Algebra with Applications Download

  • Author: Gareth Williams
  • Publisher: Jones & Bartlett Publishers
  • ISBN: 1449666329
  • Category : Mathematics
  • Languages : en
  • Pages : 532

Revised and edited, Linear Algebra with Applications, Seventh Edition is designed for the introductory course in linear algebra and is organized into 3 natural parts. Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of R, matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on this material, introducing the concept 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 many of the important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition. Offering 28 core sections, the Seventh Edition successfully blends theory, important numerical techniques, and interesting applications making it ideal for engineers, scientists, and a variety of other majors.


Applied Linear Algebra and Matrix Methods

Applied Linear Algebra and Matrix Methods

PDF Applied Linear Algebra and Matrix Methods Download

  • Author: Timothy G. Feeman
  • Publisher: Springer Nature
  • ISBN: 303139562X
  • Category : Mathematics
  • Languages : en
  • Pages : 330

This textbook is designed for a first course in linear algebra for undergraduate students from a wide range of quantitative and data driven fields. By focusing on applications and implementation, students will be prepared to go on to apply the power of linear algebra in their own discipline. With an ever-increasing need to understand and solve real problems, this text aims to provide a growing and diverse group of students with an applied linear algebra toolkit they can use to successfully grapple with the complex world and the challenging problems that lie ahead. Applications such as least squares problems, information retrieval, linear regression, Markov processes, finding connections in networks, and more, are introduced on a small scale as early as possible and then explored in more generality as projects. Additionally, the book draws on the geometry of vectors and matrices as the basis for the mathematics, with the concept of orthogonality taking center stage. Important matrix factorizations as well as the concepts of eigenvalues and eigenvectors emerge organically from the interplay between matrix computations and geometry. The R files are extra and freely available. They include basic code and templates for many of the in-text examples, most of the projects, and solutions to selected exercises. As much as possible, data sets and matrix entries are included in the files, thus reducing the amount of manual data entry required.


Numerical Linear Algebra in Signals, Systems and Control

Numerical Linear Algebra in Signals, Systems and Control

PDF Numerical Linear Algebra in Signals, Systems and Control Download

  • Author: Paul Van Dooren
  • Publisher: Springer Science & Business Media
  • ISBN: 9400706022
  • Category : Technology & Engineering
  • Languages : en
  • Pages : 481

The purpose of Numerical Linear Algebra in Signals, Systems and Control is to present an interdisciplinary book, blending linear and numerical linear algebra with three major areas of electrical engineering: Signal and Image Processing, and Control Systems and Circuit Theory. Numerical Linear Algebra in Signals, Systems and Control will contain articles, both the state-of-the-art surveys and technical papers, on theory, computations, and applications addressing significant new developments in these areas. The goal of the volume is to provide authoritative and accessible accounts of the fast-paced developments in computational mathematics, scientific computing, and computational engineering methods, applications, and algorithms. The state-of-the-art surveys will benefit, in particular, beginning researchers, graduate students, and those contemplating to start a new direction of research in these areas. A more general goal is to foster effective communications and exchange of information between various scientific and engineering communities with mutual interests in concepts, computations, and workable, reliable practices.


Orthogonal Sets and Polar Methods in Linear Algebra

Orthogonal Sets and Polar Methods in Linear Algebra

PDF Orthogonal Sets and Polar Methods in Linear Algebra Download

  • Author: Enrique Castillo
  • Publisher: John Wiley & Sons
  • ISBN: 9780471328896
  • Category : Mathematics
  • Languages : en
  • Pages : 442

Dieses Lehrbuch der linearen Algebra für fortgeschrittene Studenten konzentriert sich in erster Linie auf Anwendungen. In einem unkonventionellen Ansatz betont der Autor vor allem die Zusammenhänge zwischen mathematischem Formalismus und physikalischer Realität: Einer der vier Teile des Bandes beschäftigt sich ausschließlich mit Beispielen aus der Mathematik, Physik und Ingenieurtechnik. Mit Codebeispielen in Mathematica und Java. (04/99)