Several excellent linear algebra texts make selecting a single winner especially difficult. One contender is Linear Algebra by Jim Hefferon. Hefferon’s text is exceptionally well written, with an easily accessible approach. Its companion website is also well designed, containing helpful ancillary materials such as a student solution manual, using lecture slides and Sage software. While the book generally has a very polished look, there are certain parts that look somewhat odd. Its main weakness, however, is it incompleteness: many topics from the standard linear algebra course are covered only briefly or omitted entirely. Instructors adopting this text may need to supplement the course with their own lecture notes to cover these gaps.
The second text highly recommended here is A First Course in Linear Algebra by Robert A. Beezer, mentioned earlier. While Beezer’s writing level may be too advanced for the standard first course of linear algebra—it is probably better suited for a second course—and though many of Beezer’s organizational techniques, such as the acronym numbering system, are distracting, Beezer’s linear algebra textbook is nevertheless one of the finest pieces of OER in the mathematics discipline. In fact, Beezer’s text, in conjunction with Judson’s abstract algebra text, were the two founding texts on AIM’s Approved Textbook list. Beezer has been an enthusiastic advocate for open mathematics curriculum, and he has written extensively about best practices for incorporating mathematical computing into OER through the use of Sage via the PreTeXt project, as mentioned above. Other textbooks in this category that are worth mentioning are Linear Algebra Done Wrong by Sergei Treil and Linear Algebra by David Cherney, Andrew K. Waldon, and Tom Denton.