Introduction to Linear and Matrix Algebra Book

Introduction to Linear and Matrix Algebra

  • Author : Nathaniel Johnston
  • Publisher : Springer Nature
  • Release Date : 2021-05-19
  • Genre: Mathematics
  • Pages : 482
  • ISBN 10 : 9783030528119

Introduction to Linear and Matrix Algebra Excerpt :

This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Elements of Linear Algebra Book

Elements of Linear Algebra

  • Author : P.M. Cohn
  • Publisher : Routledge
  • Release Date : 2017-10-19
  • Genre: Mathematics
  • Pages : 240
  • ISBN 10 : 9781351452847

Elements of Linear Algebra Excerpt :

This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding.The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts.

Introduction to Linear Algebra Book
Score: 4
From 1 Ratings

Introduction to Linear Algebra

  • Author : Gilbert Strang
  • Publisher : Wellesley College
  • Release Date : 1993
  • Genre: Algebras, Linear
  • Pages : 472
  • ISBN 10 : STANFORD:36105007523389

Introduction to Linear Algebra Excerpt :

Book Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.

Linear Algebra Book
Score: 1
From 1 Ratings

Linear Algebra

  • Author : Jörg Liesen
  • Publisher : Springer
  • Release Date : 2015-11-20
  • Genre: Mathematics
  • Pages : 324
  • ISBN 10 : 9783319243467

Linear Algebra Excerpt :

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.

Linear Algebra and Geometry Book

Linear Algebra and Geometry

  • Author : Igor R. Shafarevich
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-08-23
  • Genre: Mathematics
  • Pages : 526
  • ISBN 10 : 9783642309946

Linear Algebra and Geometry Excerpt :

This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics.

Introduction to Applied Linear Algebra Book

Introduction to Applied Linear Algebra

  • Author : Stephen Boyd
  • Publisher : Cambridge University Press
  • Release Date : 2018-06-07
  • Genre: Business & Economics
  • Pages : 476
  • ISBN 10 : 9781316518960

Introduction to Applied Linear Algebra Excerpt :

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

Linear Algebra Book
Score: 4.5
From 4 Ratings

Linear Algebra

  • Author : Georgi? Evgen?evich Shilov
  • Publisher : Courier Corporation
  • Release Date : 1977-06-01
  • Genre: Mathematics
  • Pages : 404
  • ISBN 10 : 048663518X

Linear Algebra Excerpt :

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Linear Algebra Book

Linear Algebra

  • Author : Jeff Suzuki
  • Publisher : CRC Press
  • Release Date : 2021-05-04
  • Genre: Mathematics
  • Pages : 376
  • ISBN 10 : 9781000377491

Linear Algebra Excerpt :

Linear Algebra: An Inquiry-based Approach is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The Inquiry-based Approach is central to this development. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra. In our approach, students begin with a problem and develop the mathematics necessary to describe, solve, and generalize it. Thus students learn a vital skill for the 21st century: the ability to create a solution to a problem. This text is offered to foster an environment that supports the creative process. The twin goals of this textbook are: Providing opportunities to be creative, Teaching "ways of thinking" that will make it easier for to be creative. To motivate the development of the concepts and techniques of linear algebra, we include more than two hundred Activities on a wide range of problems, from purely mathematical questions, through applications in biology, computer science, cryptography, and more. Table of Contents Introduction and Features For the Student . . . and Teacher Prerequisites Suggested Sequences 1. Tuples and Vectors 2. Systems of Linear Equations 3. Transformations 4. Matrix Algebra 5. Vector Spaces 6. Determinants 7. Eigenvalues and Eigenvectors 8. Decomposition 9. Extras Bibliography Index Bibliography Jeff Suzuki is Associate Professor of Mathematics at Brooklyn College and holds a Ph.D. from Boston University. His research interests include mathematics education, history of mathematics, and the application of mathematics to society and technology. He is a two-time winner of the prestigious Carl B. Allendoerfer Award for expository writing. His publications have appeared in The College Mathematics Journals; Mathematics Magazine; Mathematics Teacher; and the American Mathematical Society's blog on teaching and learning mathematics. His YouTube channel ( includes videos on mathema

Linear Algebra as an Introduction to Abstract Mathematics Book

Linear Algebra as an Introduction to Abstract Mathematics

  • Author : Isaiah Lankham
  • Publisher : World Scientific Publishing Company
  • Release Date : 2015-11-30
  • Genre: Mathematics
  • Pages : 208
  • ISBN 10 : 9789814723794

Linear Algebra as an Introduction to Abstract Mathematics Excerpt :

This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.

Linear Algebra for Everyone Book

Linear Algebra for Everyone

  • Author : Gilbert Strang
  • Publisher : Wellesley-Cambridge Press
  • Release Date : 2020-11-26
  • Genre: Mathematics
  • Pages : 368
  • ISBN 10 : 1733146636

Linear Algebra for Everyone Excerpt :

Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.

Matrices and Linear Algebra Book

Matrices and Linear Algebra

  • Author : Hans Schneider
  • Publisher : Courier Corporation
  • Release Date : 2012-06-08
  • Genre: Mathematics
  • Pages : 432
  • ISBN 10 : 9780486139302

Matrices and Linear Algebra Excerpt :

Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues, and differential equations. Includes numerous exercises.

Abstract Algebra Book

Abstract Algebra

  • Author : Jonathan K. Hodge
  • Publisher : CRC Press
  • Release Date : 2013-12-21
  • Genre: Mathematics
  • Pages : 595
  • ISBN 10 : 9781466567085

Abstract Algebra Excerpt :

To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how mathematicians think. The book can be used in both rings-first and groups-first abstract algebra courses. Numerous activities, examples, and exercises illustrate the definitions, theorems, and concepts. Through this engaging learning process, students discover new ideas and develop the necessary communication skills and rigor to understand and apply concepts from abstract algebra. In addition to the activities and exercises, each chapter includes a short discussion of the connections among topics in ring theory and group theory. These discussions help students see the relationships between the two main types of algebraic objects studied throughout the text. Encouraging students to do mathematics and be more than passive learners, this text shows students that the way mathematics is developed is often different than how it is presented; that definitions, theorems, and proofs do not simply appear fully formed in the minds of mathematicians; that mathematical ideas are highly interconnected; and that even in a field like abstract algebra, there is a considerable amount of intuition to be found.

Linear Algebra Book

Linear Algebra

  • Author : Belkacem Said-Houari
  • Publisher : Birkhäuser
  • Release Date : 2017-10-04
  • Genre: Mathematics
  • Pages : 384
  • ISBN 10 : 9783319637938

Linear Algebra Excerpt :

This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing the necessary concepts of eigenvalues and eigenvectors, as well as the theory of symmetric and orthogonal matrices. Each idea presented is followed by examples. The book includes a set of exercises at the end of each chapter, which have been carefully chosen to illustrate the main ideas. Some of them were taken (with some modifications) from recently published papers, and appear in a textbook for the first time. Detailed solutions are provided for every exercise, and these refer to the main theorems in the text when necessary, so students can see the tools used in the solution.

A First Course in Linear Algebra Book

A First Course in Linear Algebra

  • Author : Kenneth Kuttler
  • Publisher : Unknown
  • Release Date : 2020
  • Genre: Algebras, Linear
  • Pages : 586
  • ISBN 10 : OCLC:1252786692

A First Course in Linear Algebra Excerpt :

"A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.

Introduction to linear algebra Book

Introduction to linear algebra

  • Author : Gordon Mills
  • Publisher : Transaction Publishers
  • Release Date : 2007-08-01
  • Genre: Mathematics
  • Pages : 226
  • ISBN 10 : 9781412826563

Introduction to linear algebra Excerpt :

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.