Linear Algebra

A Free text, with complete solutions, for a standard US undergraduate course

Jim Hefferon
Mathematics Department, Saint Michael's College
jhefferon at smcvt.edu

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.

Highlights

• The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues.
• It is Free. The book is Freely available, including its source.
• What makes it stand out? The approach is developmental. Although it covers the requisite material by proving things, it does not assume that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise each student's level of mathematical maturity.
• It has extensive exercise sets, with worked answers to all exercises. Some of the material described on the web as a book is really someone's lecture notes. Those are fine but from notes to a book is a long jump. Part of the difference includes things like an index and diagrams but the most important difference is that in this text subsections have perhaps two dozen exercises, spanning a range of difficulty. These come with complete answers, including the proof questions, that are also Freely available, in source form.
• Popular. This book has been downloadable since 1996 and has been used in hundreds of classes at many schools, as well as by many individuals for independent study.
• Applications. Each chapter finishes with four or five short discussions of supplemental topics. These are good for independent reading or projects, or for small group work.
• Extras. You can get beamer slides to use in class, and a lab manual that supplements the material in the text.
• Prerequisite: typically a semester of calculus (some examples use the derivative operation).
• Reviews. I know of four: the Mathematical Association of America review, the American Institute of Mathematics, one from a site for free texts, and a blog.

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).

License

This text is Free. Use it under either the GNU Free Documentation License or the 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{sjones@example.com}.}" (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 smcvt.edu.

Site Information

This site Joshua is located in the Mathematics Department of Saint Michael's College in Colchester, Vermont USA.

Joshua runs under Linux

Open Source software is a great idea. This project would not have gotten done without it.

(Credit for the logo to Matt Ericson.)