A true linear algebra textbook with extensive exercises and a complete answer key. Written by Jim Hefferon, professor at Saint Michael’s College, it also has classroom slides and a lab manual. He has offered the textbook freely online since 1996 and it had been updated on 2014-Dec-25, the last time I visited in the spring of 2015.

In writing his linear algebra textbook, Hefferon hoped to blend computational aspects of linear algebra with proofs and avoid some of the difficulties students often have with traditional linear algebra texts. He has also provided real world examples of how the mathematics can be utilized. (Something my college linear algebra textbook author certainly didn’t bother to do.) Additionally, Hefferon has presented the material to help students begin the transition from calculational mathematics to more theoretical mathematics.

The text is designed for an undergraduate level course in linear algebra. The prerequisite is a semester of calculus as some examples use the derivative operation. Hefferon admires students who take on his text as a self-study course. To aid those students, he offers something I have not seen in other textbooks that I have reviewed for The Free Textbook List – a timetable for self-study so students can pace themselves and take their time going through the material.

## Table of Contents for Linear Algebra Textbook

- Chapter One: Linear Systems
- Solving Linear Systems
- Linear Geometry
- Reduced Echelon Form
- Vector Spaces
- Definition of Vector Space
- Linear Independence
- Basis and Dimension
- Chapter Three: Maps Between Spaces
- Isomorphisms
- Homomorphisms
- Computing Linear Maps
- Matrix Operations
- Change of Basis
- Projection
- Chapter Four: Determinants
- Definition
- Geometry of Determinants
- Laplace’s Formula
- Chapter Five: Similarity
- Complex Vector Spaces
- Similarity
- Nilpotence
- Jordan Form
- Appendix

View this Free Online Material at the source:

Linear Algebra