# Linear Algebra

Written by: Jim Hefferon (Saint Michael's College)

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.

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