Linear Algebra

by Jim Hefferon

This text covers a standard first Gauss’s Method, vector spaces, linear maps and matrices, determinants, and eigenvalues and eigenvectors. In addition, each chapter ends with some brief topics, such as applications. What sets it apart is careful motivation, many examples, and extensive exercise sets. Together, these help each student master the material of the course and also help an instructor develop that student’s level of mathematical maturity.

Genres: Mathematics, Textbooks, Nonfiction, Algebra, School

Paperback

First published June 1, 2009

Reviews

[Kaung Si Thu · Rating 5 out of 5]

I am editing my review from some years ago. Per standard curriculum, Linear Algebra is the bridge where students start learning the notion of abstraction rather than mechanical computations. After using this book to teach Linear Algebra, I'd say this one and Linear Algebra done right should be enough for your undergraduate Linear Algebra.
Contentwise, the book only covers up to discovering the canonical form of similarity classes of matrices (namely Jordan Form) by breaking down the vector spaces into generalized null spaces. The pro and con about the book is that it deploys developmental approach so starting from an arbitrary chapter might not be a good idea but at the same time, it motivates why we are studying the order given in the text so students won't get lost during transitions of chapters.

[Jessica Austin · Rating 5 out of 5]

If you had to pick a single math topic to study before entering robotics, linear algebra would be it. This book is particularly good because it starts with solving systems of equations, defining spaces, and creating functions and maps between spaces–and only after this foundation is laid does it introduce matrices as a convenient form for dealing with these concepts.

Plus, it's available for free online!

[kf · Rating 3 out of 5]

This semester, my introductory Linear Algebra course was based entirely around Richard Hill's textbook, which makes linear algebra much more difficult than it need be. Jim Hefferon's text was immensely helpful, regularly clarifying topics that I struggled with using other references. Hefferon's justifications are unambiguous, and a wealth of examples are provided. Plus, the ebook version is free!

[Mike · Rating 4 out of 5]

In the typically awful genre of math textbooks, this one is pretty good. It's fairly readable, I was able to learn most topics straight from the book, and it separates out the material well, with the core text focused on the essentials and with supplementary sections that covered all of the ancillary relevant topics that I wanted to learn more about (e.g. Markov chains). It made it easy to page right through less core topics that were of less personal interest (but, another reader would find some of those useful while finding some that I found useful extraneous). It has plenty of examples and some good sample problems (seventy-five percent of the solutions are written out in a way that made perfect sense to me... 25% not so much, but that's a well above-average breakdown).

The book comes with the added bonus of being available in print for a low cost and in e-form, with all of the supplementary materials, for free.

I can only compare it to one other Linear Algebra textbook, which it easily surpasses, but can compare it to more math texts in general (both comparing as a learner, as I was in my use of this book, and as an instructor) and it seems solidly above average in the broader math text category.

[Jim Hefferon · Rating 5 out of 5]

I'm the author. Thank you to all of the folks who wrote kind things.

The link here is not to the book's latest version, so you will miss out on the many corrections and updates, and the book cover shown here is not a version of the book that I publish. To either buy a paper copy or to get the latest electronic copy for free, please visit https://hefferon.net and follow the links there. Thanks.

[Rui · Rating 4 out of 5]

Surprisingly interesting, even compared with the other well known ones.

[Rowan King · Rating 5 out of 5]

Suitable for self-study but a good lecturer helps a lot. You can find the author's lecture series on YouTube, very helpful. And of course, it's all free!

[Rishabh · Rating 4 out of 5]

Good book to review undergrad linear algebra

[Mynk Pe · Rating 4 out of 5]

My first serious math book. Like the author promises, the book really help develope mathematical maturity for beginners. It has a nice blend of proofs and computation exercises. The book is also available for free.

[Lulu]

Linear Algebra - easier