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Linear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.

The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.

The subtitle, A Geometry Toolbox, hints at the book’s geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topic in action.

Designed for a one-semester linear algebra course at the undergraduate level, this book gives instructors the option of tailoring the course for the primary interests: math, engineering, science, computer graphics, and geometric modeling.

This practical approach to a linear algebra course, whether through classroom instruction or self-study, is unique to this book.

Instead of using the standard theorem-proof approach, the text presents many examples and instructional illustrations to help students develop a robust, intuitive understanding of the underlying concepts.

Features

• More than 120 numerical examples
• 319 illustrations
• WYSK (What You Should Know) summary of main points at the end of each chapter
• Over 200 exercises at the end of each chapter with selected solutions in an appendix
• Extensive glossary
• Robust index
• An appendix with a list of applications that appear in the text
• Mathematica® code and other materials in the downloads section
• For instructors: solutions manual, lecture slides, and test bank are available

New to the Fourth Edition

• Ten new application sections.
• A new section on change of basis. This concept now appears in several places
• Chapters 14-16 on higher dimensions are notably revised
• A deeper look at polynomials in the gallery of spaces.
• Introduces the QR decomposition and its relevance to least squares.
• Similarity and diagonalization are given more attention as are eigenfunctions.
• A longer thread on least squares, running from orthogonal projections to a solution via SVD and the pseudoinverse.
• More applications for PCA have been added.
• More examples, exercises, and more on the kernel and general linear spaces.

Table of Contents

Preface

1. Descartes’ Discovery
2. Here and There: Points and Vectors in 2D
3. Lining Up: 2D Lines
4. Changing Shapes: Linear Maps in 2D
5. 2 × 2 Linear Systems
6. Moving Things Around: Affine Maps in 2D
7. Eigen Things
8. 3D Geometry
9. Linear Maps in 3D
10. Affine Maps in 3D
11. Interactions in 3D
12. Gauss or Linear Systems
13. Alternative System Solvers
14. General Linear Spaces
15. Eigen Things Revisited
16. The Singular Value Decomposition
17. Breaking It Up: Triangles
18. Putting Lines Together: Polylines and Polygons
19. Conics
20. Curves Appendices A. Applications B. Glossary C. Select Exercise Solutions

The figures are not included as window dressing, in fact they play an important role in bringing the reader to a robust understanding of the mathematics. However they are not only instructional, they are also fun!