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.

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

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.
  • A list of applications has been added in Appendix A.

The book gives instructors the option of tailoring the course for the primary interests of their students: mathematics, engineering, science, computer graphics, and geometric modeling.

chapter 1|14 pages

Descartes' Discovery

chapter 2|26 pages

Here and There: Points and Vectors in 2D

chapter 3|26 pages

Lining Up: 2D Lines

chapter 4|34 pages

Changing Shapes: Linear Maps in 2D

chapter 5|34 pages

2 × 2 Linear Systems

chapter 6|18 pages

Moving Things Around: Affine Maps in 2D

chapter 7|24 pages

Eigen Things

chapter 8|20 pages

3D Geometry

chapter 9|32 pages

Linear Maps in 3D

chapter 10|20 pages

Affine Maps in 3D

chapter 11|18 pages

Interactions in 3D

chapter 12|36 pages

Gauss for Linear Systems

chapter 13|28 pages

Alternative System Solvers

chapter 14|34 pages

General Linear Spaces

chapter 15|32 pages

Eigen Things Revisited

chapter 16|32 pages

The Singular Value Decomposition

chapter 17|14 pages

Breaking It Up: Triangles

chapter 19|14 pages


chapter 20|18 pages