Textbook

Elementary Linear Algebra: Applications Version, 10th Edition

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Elementary Linear Algebra 10^th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. Technology also is not required, but for those who would like to use MATLAB, Maple, or Mathematica, or calculators with linear algebra capabilities, exercises are included at the ends of chapters that allow for further exploration using those tools.

A concluding chapter covers twenty applications of linear algebra drawn from business, economics, physics, computer science, ecology, genetics, and other disciplines. The applications are independent and each includes a list of mathematical prerequisites.

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Table of Contents

CHAPTER 1 SYSTEMS OF LINEAR EQUATIONS AND MATRICES

CHAPTER 2 DETERMINANTS

CHAPTER 3 EUCLIDEAN VECTOR SPACES

CHAPTER 4 GENERAL VECTOR SPACES

CHAPTER 5 EIGNVALUES AND EIGENVECTORS

CHAPTER 6 INNER PRODUCT SPACES

CHAPTER 7 DIAGONALIZATION AND QUADRATIC FORMS

CHAPTER 8 LINEAR TRANSFORMATIONS

CHAPTER 9 NUMERICAL METHODS

CHAPTER 10 APPLICATIONS OF LINEAR ALGEBRA

New To This Edition

More basic applications are covered throughout
Section-end Concept Review helps students to review and prepare for exams
Skills listed at the end of every section are learning objectives that students and professors can use to measure progress
True/false exercises quickly assess conceptual understanding and logical reasoning
Chapters 3 and 4 from the 9^th are combined to form a single chapter on Euclidean vector spaces, providing more compact coverage and facilitating earlier introduction of general vector spaces
Eigenvalues and eigenvectors are introduced earlier, in chapter 5, making it easier for instructors who want to spend more time on these important topics
Chapter 9 focuses on numerical approaches that better reflect current usage of computers

Hallmark Features

Highlights Relationships among Concepts – By continually revisiting the web of relationships among systems of equations, matrices, determinants, vectors, linear transformations, and eigenvalues, Anton helps students to perceive linear algebra as a cohesive subject rather than as a collection of isolated definitions and techniques.

Proof Sketches – Students sharpen their mathematical reasoning skills and understanding of proofs by filling in justifications for proof steps in some exercises.

Emphasizes Visualization – Geometric aspects of various topics are emphasized, to support visual learners, and to provide an additional layer of understanding for all students. The geometric approach naturally leads to contemporary applications of linear algebra in computer graphics that are covered in the text.

Mathematically Sound – Mathematical precision appropriate for mathematics majors is maintained in a book whose explanations and pedagogy meet the needs of engineering, science, and business/economics students.