PNG image: cover of Linear Algebra

Linear Algebra

A Free text for a standard US undergraduate course

Jim Hefferon
Mathematics and Statistics Department
Saint Michael's College
jhefferon at

Linear Algebra is a text for a first US undergraduate Linear Algebra course. You can use it as a main text, as a supplement, or for independent study.

It is Free. The book, the complete answers to all exercises, classroom presentation slides, and a lab manual using Sage, are all available for download, as well as for purchase.

The third edition incorporates many suggestions sent by users, including many more beginning exercises, and a new Topic on coupled oscillators and eigenvalues.


Get Linear Algebra

Here is the current version of the text and the answers to exercises. Save these files in the same directory so that clicking on an exercise takes you to its answer and clicking on an answer takes you to the exercise. (You need a PDF reader that supports this; one is Adobe Reader.)

You can get a paper copy, an official one, for just about the cost of media, about $22. You can click on the link to Amazon, just below. Or, you can use ISBN-13: 978-1944325039 at your favorite site. (Bookstores can buy from NACSCORP or from Ingram via LightningSource.)

If you are teaching out of this text then have a look at the beamer slides for classroom presentation. These are compiled from the text source, so the theorems and definitions have the exact same wording. But the slides use different examples than the text so that students see twice as many. Along with those is a version of the slides without the pauses, for handing out or posting in your learning management system. (Those slides omit some proofs in favor of examples; you can also get a version that includes all proofs.)

Linear Algebra also has a supplemental, optional, lab manual using Sage.

If you are into LaTeX then you may be interested that Linear Algebra once again has a source repository.

Finally, if you find the book useful then you could make a contribution. This is entirely optional but you'd be surprised at the expenses a person runs into giving things away; contributions help with things like examination copies for conferences. I'll suggest $5 but for whatever you send, thank you!

Additional material

Prof Harold W. Ellingsen of SUNY Potsdam has shared his Matrix Arithmetic, for teachers who want to cover matrix operations after the first chapter (the book covers them in the third chapter as part of linear maps). It is under a Free license, and you can get the LaTeX source.

You can also get the problems and their solutions that I assigned for take home work when I taught the class in the Fall of 2014.

The prior edition of Linear Algebra

The second edition of Linear Algebra is still available, for someone in a legacy situation: book and answers. To use the hyperlinking between questions and answers, rename these files "book.pdf" and "jhanswer.pdf" and put them in the same directory,


This text is Free. Use it under either the GNU Free Documentation License or the Creative Commons License Creative Commons Attribution-ShareAlike 2.5 License, at your discretion.

For bookstores: thank you for being concerned about my rights. I give instructors permission to make copies of this material, either electronic or paper, and give or sell those to students. But first note that for very little money you can get a paper copy from Amazon, or NACSCORP, or directly from Ingram via LightningSource, using ISBN-13: 978-1944325039.

Please don't order used or unofficial copies since they can have significantly different content and pagination. With the current edition at pretty much the price of media, any savings from old versions are tiny compared to the cost of confusion, particularly confusion to me since I get contacted about already-fixed bugs. The current version says "Third edition" on the front cover (it also says 2017-Jan-01 at the end of the Preface).

For instructors who want to modify the text. Please, feel free. But as a favor I ask that you include a statement about your modifications. That way people making reports know who to write. Putting something like this on the cover would be great: \fbox{\parbox{0.75\textwidth}{The material in the second appendix, on induction, has been added by Professor Jones of UBU. For any reports about this material contact \url{}.}}

Can You Help With Linear Algebra?

I am glad to hear from both teachers and students. I enjoy hearing about the experience that folks have with the book and I find suggestions helpful, especially bug reports. I save these and periodically revise.

If you have something that you are able to share back then I'd be glad to take a look. For instance, I would love to have a topic on Machine Learning, or some sub-topic such as dimension reduction. Of course, I reserve the ability to choose whether to edit or include it. I gratefully acknowledge all the contributions that I use, or I can keep you anonymous.

In particular, I would welcome exams or problem sets. Some instructors have questions about using a text where the answers to the exercises are downloadable. (I can't resist noting that for any widely-available text any college student can get from the Internet copies of the answers. Also, in the past I tried witholding the answers and asking class instructors to email me for copies but that left me trying to determine identity via email, which is just not practical.) Thus additional sets of exercises without answers would answer the requests of some instructors. If you could contribute your TeX or LaTeX source that'd be great because then instructors could cut and paste.

I would also welcome contrbutions related to the emerging electronic tools. For instance, if you have sets of questions that are suitable for Moodle quizzes and that you could share with other users of this book then write me and we can see about making them available. The same holds for WeBWorK problem sets. And, I would be glad to be able to include in the distribution a deck of Anki cards.

My email is at the top of this page.

I have two other texts. Both are Free. My Introduction to Proofs is for a proofs course taught using the Inquiry-Based method (also known as the Discovery method or the Moore method). It covers elementary number theory, sets, functions, and relations. My Theory of Computation covers Turing Machines, the Halting problem, Automata, and Complexity. It is now beta, being classroom-tested, and is under active development.

In addition, you may also like my Cheat Sheet for LaTeX math, aimed at undergraduates but useful for anyone.

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Site Information

This site Joshua is located in the Mathematics Department of Saint Michael's College in Colchester, Vermont USA.

Joshua runs under Linux

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Open Source software is a great idea. This project would not have gotten done without it.

(Credit for the logo to Matt Ericson.)