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 these 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 such as Adobe Reader. (The cover artwork does 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 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 I advise against used copies since they are likely to be outdated and have significantly different content and pagination. Besides, a new copy costs $20 so any savings are tiny compared to the cost of potential confusion.)

Note. I have just sent in a new version to be printed (2014-Dec-22). There will be a few days during which the paper and electronic versions are out of sync. I will erase this paragraph when that is no longer true. The PDF above is the new version of the book; the PDF of the old version is below. They differ mainly in bug fixes and the addition of a few computational excercises in Chapters Three and Five..

You may also be interested in beamer slides for classroom presentation which draw from the text source but use different examples, and omit some proofs in favor of examples. (There is a version of the slides that includes all proofs.) These have been greatly improved since the prior version. There is also 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 PDF of the book's printed version, along with its cover. Probably you don't want this; the book above is the same, page for page, as here but includes with hyperlinks and excludes a title page.

If you want the prior version. You can get a PDF of the March 2014 version along with a PDF of the associated answers. (Rename them to book.pdf and jhanswer.pdf to make cross-referencing work.) This PDF only makes snese for people who have a paper version of the book dated March of 2014 and who want to get an electronic version, perhaps 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: 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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