This book grew out of a series of twenty five lecture notes for a sophomore linear algebra class taught at the University of California, Davis. The audience was primarily engineering students and students of pure sciences, some of whom may go on to major in mathematics. It was motivated by the lack of a book that taught students basic structures of linear algebra without overdoing mathematical rigor or becoming a mindless exercise in crunching recipes at the cost of fundamental understanding. In particular we wanted a book that was suitable for all students, not just math majors, that focussed on concepts and developing the ability to think in terms of abstract structures in order to address the dizzying array of seemingly disparate applications that can all actually be addressed with linear algebra methods.

In addition we had practical concerns. We wanted to offer students a online version of the book for free, both because we felt it our academic duty to do so, but also because we could seamlessly link an online book to a myriad of other resources–in particular WeBWorK exercises and videos. We also wanted to make the LaTeX source available to other instructors so they could easily customize the material to fit their own needs. Finally, we wanted to restructure the way the course was taught, by getting the students to direct most of their effort at more difficult problems where they had to think through concepts, present well-thought out logical arguments and learn to turn word problems into ones where the usual array of linear algebra recipes could take over.