Practical Linear Algebra: A Geometry Toolbox, Fourth Edition
Gerald Farin & Dianne Hansford
A K Peters/CRC Press
592 Pages, 319 B/W Illustrations
ISBN: 9780367507848


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.


New to the Fourth Edition

Table of Contents

  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
A. Applications
B. Glossary
C. Select Exercise Solutions

Phoenix rotate

What's different about our approach to Linear Algebra?

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!

Least squares  affine map Quadratic form


Our motivation for writing PLA is described in our Fall 2005 TIES Magazine (design and technology education) article, "A Practical Approach to Teaching Linear Algebra."