PNG image: cover of Linear Algebra

Linear Algebra

A Free text for a standard US undergraduate course

Jim Hefferon
Mathematics 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 with the answers to all exercises, as well as beamer slides for classroom use and a lab manual using Sage, are all available for download, as well as for purchase.


Download Linear Algebra

Here is the current version of Linear Algebra and its answers to exercises. Save these files in the same directory so that clicking on an exercise sends you to its answer and clicking on an answer sends you to the exercise. (You must use a PDF reader that supports this, such as Adobe Reader.)

If you prefer a paper copy then you can buy an official one using ISBN-13: 978-0989897563 from a number of sources, including Amazon; the price there is $20. (Bookstores can buy from NACSCORP or from Ingram via LightningSource.)

If you are a teacher then have a look at the beamer slides for classroom presentation. These draw from the text source; for instance, theorems appear referenced with their number from the text. But they use different examples so students see twice as many. (Those slides omit some proofs in favor of illustrative examples; there is also a version that includes all proofs.)

There is also a lab manual that supplements the text material using Sage.

Covering it all You could also get the book's cover and a PDF of the book's printed version, if for some reason you are keen.

Additional material

Prof Harold W. Ellingsen of SUNY Potsdam has shared his Matrix Arithmetic, for people who want to cover matrix operations after the book's first chapter (the book covers them in the fourth chapter). 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 next edition of Linear Algebra

The third edition of Linear Algebra, dated 2016-Nov-24, incorporates many suggestions sent by users of the second edition. Differences include many more beginning exercises, a new Topic on Coupled Oscillators and eigenvalues, and a question bank. Thank you to everyone who wrote with bug fixes and suggestions.

Note: If you are teaching a class out of the text, or taking a class in which your instructor has adopted the text, then you should decide whether you want to download the current edition above, or the third edition. This third edition will not be for paper sale for a short time, a week or two.

You can download third edition book and the associated answer book. The lab manual is unchanged. The draft of the classroom slides is available but they are in flux, being adjusted to conform to the new edition of the text. They will be ready by the time the new semester starts in January.

If you are into LaTeX then you will want to know that Linear Algebra once again has a source repository, this time at GitLab.


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: 978-0989897563. Please don't order used or unofficial copies since they can have significantly different content and pagination. With an up to date copy 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 is 2014-Dec-25; see the printed copy's title page or the last page of the Preface. If you have any questions, please contact me.

For instructors who want to modify the text: please, feel free. If you can share back your modifications then I'd be glad to see them, but if not that is fine. However, as a favor, I ask that you make clear which material is yours and which is from the main version of the text. I sometimes get questions or bug reports and working out what is going on gets frustrating all around unless authorship is clear. In particular, one approach that would help is changing the cover to include a statement about your modifications. Something like this would be great: " \fbox{\parbox{0.75\textwidth}{The material in the second appendix on induction is not from the main version of the text but has been added by Professor Jones of UBU. For this material contact \url{}.}}"

Can You Help With Linear Algebra?

Feel free to write me with any comments. I enjoy hearing about the experience that instructors have 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 delighted to see it. 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 reservations about using a text where the answers to the exercises are downloadable. (I can't resist noting here that this objection is misguided: any college student can in seconds get from the Internet copies of the answers to any widely-available text. I'll also say that 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.

My email is at the top of this page.

You may also like my Introduction to Proofs, an Inquiry-Based approach text, also Freely available. It is for a proofs course taught using Moore method, which is known in other fields as Inquiry-Based or the Discovery Method.
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This site Joshua is located in the Mathematics Department of Saint Michael's College in Colchester, Vermont USA.

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