Practical linear algebra : a geometry toolbox / Gerald Farin and Dianne Hansford.

Includes bibliographical references and index.

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 for 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
Appendix A. Glossary;
Appendix B. Selected Exercise Solutions;
Bibliography;
Index.

Practical Linear Algebra covers all the concepts in a traditional undergraduate-level linear algebra course, but with a focus on practical applications. The book develops these fundamental concepts in 2D and 3D with a strong emphasis on geometric understanding before presenting the general (n-dimensional) concept. The book does not employ a theorem/proof structure, and it spends very little time on tedious, by-hand calculations (e.g., reduction to row-echelon form), which in most job applications are performed by products such as Mathematica. Instead the book presents concepts through examples and applications.