Linear Algebra: Concepts and Methods

Author: Martin Anthony,Michele Harvey
Publisher: Cambridge University Press
ISBN: 0521279488
Category: Mathematics
Page: 516
View: 1680
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.

Matemáticas para la economía y las finanzas

Author: Martin Anthony,Norman Biggs,Ernesto Junquera
Publisher: Ediciones AKAL
ISBN: 9788483232484
Category: Business & Economics
Page: 422
View: 602
Las matemáticas se han convertido en una herramienta de trabajo indispensable para el diseño de modelos en el ámbito de las ciencias económicas, las finanzas, los negocios y la dirección de empresas. Tanto su lenguaje como sus técnicas permiten afrontar problemas que, de otra manera, serían difíciles, de resolver. Este libro aborda los conceptos matemáticos de frecuente aplicación en el campo de las ciencias económicas y de las finanzas, y hace hincapié en la forma en que las matemáticas se relacionan con ellas. tales relaciones se ilustran por medio de abundantes ejemplos y ejercicios que ayudan a profundizar en su comprensión. Por su característica de introducción, amplia y clara, y por su cuidado desarrollo metodológico, este manual se convertirá en texto indispensable para estudiantes de ciencias económicas y matemáticas.

Linear Algebra and Its Applications

Author: Gilbert Strang
Publisher: Academic Press
ISBN: 1483265110
Category: Mathematics
Page: 428
View: 6234
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.

Linear Algebra with Applications

Author: Gareth Williams
Publisher: Jones & Bartlett Publishers
ISBN: 1449679544
Category: Mathematics
Page: 589
View: 2936
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

Mathematics for Physicists

Introductory Concepts and Methods
Author: Alexander Altland,Jan von Delft
Publisher: Cambridge University Press
ISBN: 1108471226
Category: Mathematics
Page: 600
View: 800
Introduces fundamental concepts and computational methods of mathematics from the perspective of physicists.

Differential Equations and Linear Algebra

Author: Charles Henry Edwards,David E. Penney
Publisher: Prentice Hall
ISBN: 9780136054252
Category: Mathematics
Page: 762
View: 9872
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.

Calculus: Concepts and Methods

Author: Ken Binmore,Joan Davies
Publisher: Cambridge University Press
ISBN: 1139643622
Category: Mathematics
Page: N.A
View: 7274
The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.

A Bridge To Linear Algebra

Author: Mikusinski Piotr,Atanasiu Dragu
Publisher: World Scientific
ISBN: 9811200246
Category: Mathematics
Page: 508
View: 6884
The book makes a first course in linear algebra more accessible to the majority of students and it assumes no prior knowledge of the subject. It provides a careful presentation of particular cases of all core topics. Students will find that the explanations are clear and detailed in manner. It is considered as a bridge over the obstacles in linear algebra and can be used with or without the help of an instructor.While many linear algebra texts neglect geometry, this book includes numerous geometrical applications. For example, the book presents classical analytic geometry using concepts and methods from linear algebra, discusses rotations from a geometric viewpoint, gives a rigorous interpretation of the right-hand rule for the cross product using rotations and applies linear algebra to solve some nontrivial plane geometry problems.Many students studying mathematics, physics, engineering and economics find learning introductory linear algebra difficult as it has high elements of abstraction that are not easy to grasp. This book will come in handy to facilitate the understanding of linear algebra whereby it gives a comprehensive, concrete treatment of linear algebra in R² and R³. This method has been shown to improve, sometimes dramatically, a student's view of the subject.

Elementary Linear Algebra

Author: Howard Anton
Publisher: John Wiley & Sons
ISBN: 0470458216
Category: Mathematics
Page: 592
View: 2052
When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning.

Matrix Algebra for Linear Models

Author: Marvin H. J. Gruber
Publisher: John Wiley & Sons
ISBN: 1118592557
Category: Mathematics
Page: 392
View: 4303
A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.

Linear Algebra and Projective Geometry

Author: Reinhold Baer
Publisher: Courier Corporation
ISBN: 0486154661
Category: Mathematics
Page: 336
View: 6533
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.

Orthogonal Sets and Polar Methods in Linear Algebra

Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming
Author: Enrique Castillo,Angel Cobo,Francisco Jubete,Rosa Eva Pruneda
Publisher: John Wiley & Sons
ISBN: 1118031148
Category: Mathematics
Page: 422
View: 2206
A unique, applied approach to problem solving in linearalgebra Departing from the standard methods of analysis, this unique bookpresents methodologies and algorithms based on the concept oforthogonality and demonstrates their application to both standardand novel problems in linear algebra. Covering basic theory oflinear systems, linear inequalities, and linear programming, itfocuses on elegant, computationally simple solutions to real-worldphysical, economic, and engineering problems. The authors clearlyexplain the reasons behind the analysis of different structures andconcepts and use numerous illustrative examples to correlate themathematical models to the reality they represent. Readers aregiven precise guidelines for: * Checking the equivalence of two systems * Solving a system in certain selected variables * Modifying systems of equations * Solving linear systems of inequalities * Using the new exterior point method * Modifying a linear programming problem With few prerequisites, but with plenty of figures and tables,end-of-chapter exercises as well as Java and Mathematica programsavailable from the authors' Web site, this is an invaluabletext/reference for mathematicians, engineers, applied scientists,and graduate students in mathematics.

Advanced Linear Algebra for Engineers with MATLAB

Author: Sohail A. Dianat,Eli Saber
Publisher: CRC Press
ISBN: 1420095242
Category: Mathematics
Page: 346
View: 7136
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.

Introduction to Linear Algebra and Differential Equations

Author: John W. Dettman
Publisher: Courier Corporation
ISBN: 9780486651910
Category: Mathematics
Page: 404
View: 6101
Excellent introductory text for students with one year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Numerical Linear Algebra

Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120334361
Category: Mathematics
Page: 616
View: 2902
This well-organized text provides a clear analysis of the fundamental concepts of numerical linear algebra. It presents various numerical methods for the basic topics of linear algebra with a detailed discussion on theory, algorithms, and MATLAB implementation. The book provides a review of matrix algebra and its important results in the opening chapter and examines these results in the subsequent chapters. With clear explanations, the book analyzes different kinds of numerical algorithms for solving linear algebra such as the elimination and iterative methods for linear systems, the condition number of a matrix, singular value decomposition (SVD) of a matrix, and linear least-squares problem. In addition, it describes the Householder and Givens matrices and their applications, and the basic numerical methods for solving the matrix eigenvalue problem. Finally, the text reviews the numerical methods for systems and control. Key Features Includes numerous worked-out examples to help students grasp the concepts easily.  Provides chapter-end exercises to enable students to check their comprehension of the topics discussed.  Gives answers to exercises with hints at the end of the book.  Uses MATLAB software for problem-solving. Primarily designed as a textbook for postgraduate students of Mathematics, this book would also serve as a handbook on matrix computations for scientists and engineers.

Linear Algebra

Author: Jörg Liesen,Volker Mehrmann
Publisher: Springer
ISBN: 3319243462
Category: Mathematics
Page: 324
View: 4891
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.

Handbook of Linear Algebra

Author: Leslie Hogben
Publisher: CRC Press
ISBN: 1420010573
Category: Mathematics
Page: 1400
View: 6204
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 accessibl

Algebra lineal

Author: Seymour Lipschutz
Publisher: N.A
ISBN: 9788476157589
Category: Mathematics
Page: 553
View: 367

Matrix Methods in Data Mining and Pattern Recognition, Second Edition

Author: Lars Elden
Publisher: SIAM
ISBN: 1611975867
Category: Mathematics
Page: 229
View: 1183
This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. This book is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.