Acknowledgments

No textbook is written in a vacuum, and a linear algebra textbook least of all. The subject has been taught and refined for the better part of two centuries, and this book stands on the shoulders of the people who taught it well.

We owe a particular debt to four reference works, each of which shaped how this book thinks about the subject. Gilbert Strang's Introduction to Linear Algebra is the source of the four-fundamental-subspaces framing that organizes Part III and recurs throughout — the insight that column space, null space, row space, and left null space are the structure on which everything else hangs. Sheldon Axler's Linear Algebra Done Right is the model for treating linear transformations, not matrices, as the primary objects, and for delaying the determinant until its geometric meaning can be earned rather than assumed. Stephen Boyd and Lieven Vandenberghe's Introduction to Applied Linear Algebra is the touchstone for taking applications seriously as mathematics rather than as decoration — least squares, regression, and data fitting as first-class material. And Jim Hefferon's Linear Algebra, generously released for free, proved that a rigorous, complete linear algebra textbook can be given away without compromise, and set a standard this book tries to honor.

This book also belongs to the broader open educational resources (OER) movement — the community of educators, mathematicians, and institutions who decided that the cost of a textbook should never be the reason a student cannot learn. The principle that good mathematical education should be free, modifiable, and shareable is not an afterthought here; it is the reason the book exists in this form at all.

In that spirit, Linear Algebra: The Mathematics of Everything is released under the Creative Commons Attribution–ShareAlike 4.0 International License (CC BY-SA 4.0), with code samples and the from-scratch toolkit/ additionally under the MIT License. You are free to copy it, adapt it, translate it, assign it, remix it into your own course, and build on it — provided you credit the source and share your derivative works under the same terms. If this book helps you, the best thanks you can offer is to pass it on, improve it, and keep it free.

Finally, to the student opening this on a screen instead of buying a two-hundred-dollar hardcover: this one is for you.