January 2024 updates: Thanks to our friends at
I'm excited to announce that there are now low-cost print
versions of the
The newest version of the book, created in December 2023,
fixed some small errors and layout issues. Nothing
substantial has changed since August 2022.
Understanding Linear Algebra is a freely
available linear algebra textbook suitable for use in a
first undergraduate linear algebra course. The text aims
to support readers as they develop their ability to reason
mathematically, their computational
fluency, and their understanding of the role that linear
algebra plays in shaping our society. It is also
designed to support an active learning classroom
Understanding Linear Algebra is written in
PreTeXt and has been endorsed by the
Open Textbook Initiative
American Institute of Mathematics.
Understanding Linear Algebra can support a
two-course introductory sequence to linear algebra.
While it is not meant to serve as an introduction to
proofs, activities and exercises support students as
they develop their ability to reason mathematically and
communicate their understanding. At my university,
our first two linear algebra courses do not require
calculus as a prerequisite, and we find that many
students thrive in it.
Understanding Linear Algebra is intended to
support active learning. Each
section begins with a preview activity for students to
complete before class and subsequently contains several
activities for students to complete in class, perhaps
working collaboratively in small groups. A solutions
manual for the activities is available upon request.
Each section contains numerous exercises from routine
review to more in-depth, conceptual questions.
Solutions are also available upon request.
The text contains numerous embedded
cells to facilitate linear algebraic computations.
Relevant Sage commands are introduced as needed and
summarized in an appendix.
Many applications are introduced and developed in depth to
build an appreciation of how linear algebra plays a
vital role in our society. These applications include
topics such as
computer animation, image compression, Google PageRank,
least squares, principal component analysis, and singular
Interactive diagrams embedded in the text help students
develop an intuitive understanding of key linear algebra
First, I hope Understanding Linear Algebra is a
valuable resource for you and your students in whatever way
you find most appropriate to use it.
I would very much like to hear from you at the
email address given below. Since the book is freely
available, it's difficult to know how many people are using
it and what value they are finding in it.
The book is in use at over 30 institutions, from R1s to
community colleges and high schools. There is a community
of instructors using ULA, and we share resources
such as online homework sets, syllabi, learning objectives,
and more. There are also solution
manuals for both the activities and exercises available upon
Please reach out to me to connect with this