Linear Algebra

Linear Algebra by Jim Hefferon is released under the GNU Free Documentation license. Electronic copies may be downloaded for free. Hardcover copies are available for the cost of manufacturing (the publisher receives no additional revenue). The book covers the material of a first undergraduate Linear Algebra course. The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: a semester of calculus. Students with three semesters of calculus can skip a few sections. The approach is developmental. It does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.