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 and the answers to exercises. If you save the two files in the same directory then clicking on an exercise sends you to its answer and clicking on an answer sends you to the exercise, if you use a PDF reader that supports this. (The cover artwork may not display correctly in some PDF renderers but it is right in Adobe Reader.)

If you prefer a paper copy then you can buy an official one from a number of internet sources, including Amazon; the price there is $20. (For bookstores: our bookstore's manager tells me that he was not allowed to buy more than four copies from Amazon and he got copies from NACSCORP; you can also get them directly from Ingram via LightningSource. I advise against used copies since they are likely to be outdated and have significantly different content and pagination.)

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.

Material of less general interest. If you are into LaTeX then you can clone the source repository. You could also get the book's printed version, which is slightly different than the version above (and slightly less suitable as an e-book), along with its cover.

New! You can get a draft of the next version along with the associated answers. (Once you get them, strip the "new", that is, rename them to book.pdf and jhanswer.pdf so that cross-referencing will work.) You can also get the new beamer slides (or the variant with all the proofs). If you are trying to decide which version to download, get these (including the new beamer slides). They incorporate the latest bug reports and in particular the slides are much improved. I will change these to be the main versions after finals when I can do some minor housekeepping.

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: 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 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 people's experiences and I find suggestions helpful, especially bug reports. I save these and periodically revise.

If you are an instructor who has some material that you are able to share back, such as the additional material above, then I'd be delighted to see it. Of course, I reserve the ability to choose whether to use 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 knows how to use the Internet to get copies of the answers to all widely-available texts. I'll also say that I have tried witholding the answers and asking class instructors to email me for copies but that left me trying to determine identity via email, which just is 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. 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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