Linear Algebra

by
Jim Hefferon
Mathematics
Saint Michael's College
Colchester, Vermont USA 05439
jhefferon at smcvt.edu

Linear Algebra is a text for a first US undergraduate Linear Algebra course. It is Free. You can use it either as a main text, as a supplement to another text, 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, in source form.
• What makes it stand out? The approach is developmental. Although the presentation is focused on covering the requisite material by proving things, it does not start with an assumption 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 a student's level of mathematical maturity.
• It has extensive exercise sets, with worked answers to all exercises Some of the material described on the Intenet as a book is really more of someone's lecture notes. Posting notes is fine, but from notes to a book is a long way. 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. All of these come with complete answers, including the proofs, 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 individuals.
• Applications. Each chapter finishes with three or four discussions of additional topics and applications. These are suitable for independent study or for small group work.
• Prerequisite: typically a semester of calculus. Someone without calculus must skip some examples.
• Reviews. I know of three: the Mathematical Association of America review, 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. Save the two files in the same directory, so that clicking on an exercise will send you to its answer and clicking on an answer will send you to its exercise. You can also get the source, if you are into LaTeX.

These files are current as of 2012-Feb-29. This is a significant upgrade from the prior version (see below if you need the prior verion). Much of the improvement comes from user feedback. Thank you to the users who contributed (see the Acknowledgements file in the source).

Alternative formatting. You can get the book formatted in Computer Modern Roman or as an ebook (caution: this one is not satisfactory since some equations do not break correctly). Please note that I do not keep these versions completely up to date, so you may want to compile them from source if you are especially keen.

Optional There is a bit of optional material. There are also some materials that were contributed by folks other than me.

The prior version of Linear Algebra

This 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: 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 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.

Can You Help With Linear Algebra?

Please feel free to drop me a note with any comments. I enjoy hearing about people's experiences and I find suggestions helpful, especially bug reports. I save these and periodically revise the copy available here.

If you are an instructor who adopts the book and you have some material that you are able to share then, again, please write me (of course, I reserve the ability to choose whether to use the material). I will gratefully acknowledge all contributions, or keep you anonymous if you like.

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 (and I failed at trying to determine over email who should get the answers, and besides, the answers instantly appeared on torrents) so additional sets of exercises would be a help. 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 I'd be interested in talking. 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.)