PNG image: cover of Linear Algebra

Linear Algebra

A Free text, with complete solutions, 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.


Here Is Linear Algebra

Click to download Linear Algebra. I suggest that you also get the answers to exercises. If you save the two files in the same directory with the names that they have now then clicking on an exercise will send you to its answer and clicking on an answer will send you to its exercise. You may also be interested in beamer slides for classroom presentation which draw from the text source, and a lab manual that supplements the text material using Sage (these two are beta).

If you are into LaTeX and want the source code then I recommend that you clone the repository (you could instead get a .zip). There is also a bit of optional material and some material that was contributed by folks other than me.

These files are for the book's, 2013-Jan-01 version. This is a significant upgrade from the 2011 version, which I will retire soon. Much of the improvement comes from user feedback. Thank you to the folks who contributed (see the Acknowledgements file in the source).

The prior version of Linear Algebra

This version is the text published by Eleven Learning. These files are from 2011-Jan-25 and include the answers to the exercises. Click to get whole book Linear Algebra (2011) along with the answers to exercises (2011). You can also get the source (2011).


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: I appreciate your 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 and prorate the price of student copies so that their copy is free.) Many schools use this text in this way. If you have further questions, don't hesitate to contact me.

If you modify the text: a number of instructors have asked if they can modify the material. Please, feel free. If you are able to share back your modifications then I'd be glad to see them. If not that is fine. However, I ask as a favor 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 about the book and having to work out what is going on could get frustrating all around unless authorship is clear. In particular, changing the cover to include a statement about your modifications would help. 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{}.}" (If you have plans for more than a minor modification, such as plans to make the material more interactive then see below.)

Can You Help With Linear Algebra?

Feel free to write me with any comments. I enjoy hearing about people's experiences and I find suggestions helpful, especially bug reports. I save these and periodically revise.

If you are an instructor who adopts the book and you have some material that you are able to share back then I'd be delighted to see it. Of course, I reserve the ability to choose whether to use the material. I gratefully acknowledge all the contributions that I use, or I can keep you anonymous if you prefer.

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 that this objection is misguided: anyone on the Internet can get copies of the answers to essentially all widely-available texts. I'll also note that 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 was not practical.) Thus additional sets of exercises, without answers, would help 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.

My email is jhefferon at

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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.)