A Portrait of Linear Algebra, 2nd Edition

The book’s great strength is that it eases very gradually into the subject, starting with very simple, concrete examples of vectors and matrices in R2 and R3 and gradually working into abstract vector spaces, with lots and lots of numerical examples and exercises throughout. The book takes a “taxonomy” approach: it defines some objects and some properties, categorizes the objects according to which properties they have, and then declares the job done. Most of the exercises have answers in the back of the book.

Table of Contents

Chapter 0. The Language Of Mathematics: Sets, Axioms, Theorems & Proofs
Chapter 1. The Canvas Of Linear Algebra: Euclidean Spaces And Subspaces
Chapter 2. Adding Movement And Colors: Linear Transformations On Euclidean Spaces
Chapter 3. From The Real To The Abstract: General Vector Spaces
Chapter 4. Peeling The Onion: The Subspace Structure Of Vector Spaces
Chapter 5. From Square To Scalar: Permutation Theory And Determinants
Chapter 6. Painting The Lines: Eigentheory, Diagonalization And Similarity
Chapter 7. Geometry In The Abstract: Inner Product Spaces
Chapter 8. Imagine That: Complex Spaces And The Spectral Theorems
Chapter 9. The Big Picture: The Fundamental Theorem Of Linear Algebra And Applications
Appendix A: The Real Number System
Appendix B: Logical Symbols And Truth Tables