No bullshit linear algebra v2 release

The NO BULLSHIT guide to LINEAR ALGEBRA is finally ready. After two years of writing and two years of editing, the book is now complete! Thanks to all the feedback from readers and the amazing attention to detail of my editor Sandy Gordon, the first print release is very polished.

No bullshit guide to linear algebra product shot

Can I see a preview?

I’ve posted an extended preview of the book here (160 pages, PDF) so you can get a feel of what’s included. I tried to make the preview useful on its own: rather than showing only a few pages from the introduction, I’ve included the definitions from all the sections, which are the most important part of the book.

If you’re not interested in reading a whole book, but just want to see the graphical representation of all the linear algebra topics, I encourage you to check the concept maps here. If you’re looking for a quick refresher on linear algebra concepts, you can check the four-page linear algebra summary here.


Why should I learn linear algebra?

Linear algebra is the foundation of science and engineering. Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, and quantum mechanics. Indeed, linear algebra offers a powerful toolbox for modelling the real world. All areas of advanced science and engineering make use of linear algebra models in one way or another. So essentially, you need to learn linear algebra if you want to do science.


Why do I need this book?

There are many great books about linear algebra that exist out there[1,2,3]. The NO BULLSHIT guide to LINEAR ALGEBRA is special because of the concise, conversational tone it is written in, the prerequisites material it includes, and the numerous exciting applications of linear algebra it discusses. This book is the result of  years of private tutoring, which makes the narrative feel much more like a conversation with a friend rather than a stuffy lecture. I know from experience that many adults don’t remember basic math topics like algebra, functions, and equations, so the book includes a comprehensive review chapter (Chapter 1) to make sure everyone is on board with the fundamentals.

The “main course” of the book (Chapters 2 through 6) consists of all the standard material covered in linear algebra courses with lots of examples, exercises, and practice problems with solutions.

The book concludes with three “dessert” chapters that discuss applications of linear algebra. We start with applications to chemistry, economics, electrical engineering, graph theory, numerical optimization, cryptography, and signal processing (Chapter 7). Next we followup with a chapter on probability theory, Markov chains, and an exploration of Google’s PageRank algorithm (Chapter 8). The book concludes with a chapter that introduces the fundamental ideas of quantum mechanics and quantum computing (Chapter 9). Many of the topics covered in chapters 7, 8, and 9 are considered “advanced” or “graduate level,” but readers of the book who’ve gained a solid grasp of linear algebra concepts will be able to learn about these exciting applications with no problem at all.


Where can I buy this book?

It depends on what you want. The eBook version costs $29 and is a pretty sweet deal since it comes with all future updates. But if you really want to learn the material, you should get the softcover print version, which is much better for focused learning, and costs about the same: \$39 – 20% off = \$31. If money isn’t a constraint for you right now, you should get the hardcover, which is printed on larger paper and has a construction that will last for decades.

Regardless of your choice of medium, you’ll be getting the same high quality book that will introduce you to the wonderful subject of linear algebra in the least intimidating way possible.

Linear algebra v2 beta release

The No bullshit guide to linear algebra files on gumroad were updated. The book is now v2 beta 2, and scheduled for release in early January 2017.

If you’re taking a linear algebra class this term, or need to know linear algebra for a more advanced class, this will be the best money you spend this semester.



Math is power. Specifically, the ability to use math models to describe real-world phenomenon and predict the future is a powerful general tool to add to you toolbox. Linear algebra has applications to many fields. In general, understanding basic math, and specifically functions of the form \(f(x)=y\) like \(x,x^2,x^3,x^n,e^x,\ln(x),\sin(x),\cos(x),\tan(x),\ldots\) opens many doors for mathematical modelling.

Linear algebra is the study of linear transformations, or vector functions of the form \(T(\vec{v}) = \vec{w}\). The linear transformations take vectors \(\vec{v}\) as inputs and produce vectors \(\vec{w}\) as outputs.  Many real-world phenomena in computer science, physics, chemistry, biology, and many other fields can be modeled as vector quantities, so linear algebra has countless applications. Linear algebra is the vector extension to your math modelling toolbox.



Everyone knows that math is useful, but people much rather leave the learning of math to other people, rather than learn math themselves. Most people imagine learning math is a difficult task, like carrying big bags of potatoes up a steep hill. Surely, such hard work is not for everyone, and we should delegate all the potato-carrying to experts in the field (mathematicians, scientists, and engineers). This way of thinking gave us a modern world where only a small portion of the world is math literate. Everyone else lives in ignorance and fear of all things mathematical.

It doesn’t need to be this way. Everyone can learn math—even advanced math like linear algebra—if they follow a structured approach. Each section in the No bullshit guide to linear algebra follows the same recipe:

  • Motivation to trick readers into wanting to learn about the topic
  • Definitions of all quantities and variables relevant to the topic
  • Formulas: all the essential formulas associated with the topic are given
  • Examples that show how to use the formulas in different scenarios
  • Explanations about how the formulas are derived and how to understand them
  • Discussion about how the connections between this topic and other
  • Exercises to test your understanding of the concept
  • Links to web resources for further reading

This structure allows to get all the important information across in the shortest amount of time. The reader is free to skim through superficially, or dig in an read all the explanations. The exercises help both students and self-learners test there understanding of the material.



The No bullshit guide to linear algebra is a short textbook that covers all the standard topics of university-level linear algebra, and also discusses applications like machine learning, computer graphics, probability theory, and quantum mechanics.

You can buy the eBook bundle here ($29, includes all future updates). The book is currently being edited, so it’s likely to see some further improvements to the chapters on applications, but the main material (that which will be on a an exam) is absolutely solid now.

@Students: get in touch with me if you’d like to be a “test subject” for the new  problem sets. I wrote 50+ pages of new problems and solutions for the book, and I could use your help to double-check the answers.