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. It is Free. You can use it as a main text, as a supplement, or for independent study.


Download Linear Algebra

Here is the latest version of Linear Algebra and the answers to exercises. Save these two 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. (Of course 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 from a number of sources using ISBN-13: 978-0989897563, including Amazon; the price there is $20.

If you are teaching a class 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. (The slides linked there omit some proofs in favor of illustrative examples. There is also a version of the slides that includes all proofs.) These slides have been greatly updated with the new book version.

There is also a lab manual that supplements the text material using Sage. (Note: I don't know of anyone who has class-tested the lab so consider it a draft. If you use it then please let me know.)

For bookstores: you can get paper copies from NACSCORP or directly from Ingram via LightningSource, ISBN-13: 978-0989897563. Please avoid used or unofficial copies since they can be outdated or have significantly different content and pagination — with an up to date copy at not much more than the price of printing, any dollar savings from old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.

Material of less interest. If you are into LaTeX then you can clone the source repository. You could also get the book's cover and a PDF of the book's printed version, if for some reason you are keen.

For the prior version. You can get a 2014-March version along with its answers. Rename them to book.pdf and jhanswer.pdf to make cross-linking work. Getting these only makes sense if you have already have an old paper copy and you want an electronic version for the answers, or to put on a device.

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.


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.

To 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 copies to students. (Instructors may like to make an extra copy for themselves and pay for it by prorating the price of student copies.) Many schools use this text in this way. If you have further questions, don't hesitate to contact me.

If you 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 often 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{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 has some material that you are able to share back, such as the additional material above, then I'd be delighted to see it. (For instance, if you could write a 3-5 page Topic illustrating eigenvalues and eigenvectors by using normal modes of coupled pendulums, perhaps by descretizing the problem, and perhaps with video, why then that'd be great. Also great would be a topic on dimension reduction for Machine Learning.) 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: anyone college student can get copies of the answers to all widely-available texts off the Internet in seconds. 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 jhefferon at

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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