I’m happy to announce the No Bullshit Guide to Linear Algebra v2.2 is out. This update contains two years’ worth of text improvements based on readers’ feedback.
In this blog post I’ll summarize the changes to the book and provide some more context about why these changes were needed. I’ve included links to PDF excerpts of all the new sections[1,2,3,4] and a detailed red-blue diff that shows all edits.
Summary of changes in v2.1 → v2.2
- The eBook is now available in .pdf, .epub, and .mobi formats. Generating decent-looking ePub and Mobi files from LaTeX source with lots of math equations wasn’t easy, but I managed to build a pipeline based on TexSoup, Softcover, and Calibre that works great. See this tech blog post for more info about the eBook production pipeline.
- I added an index to the book. You can use this list of the most important math concept in the book to find the page where each concept is defined. Working on the index let to improvements to the terminology used in the book. For example, the terms coefficients, coordinates, components, and entries are now used consistently: points have coordinates, vectors have components, and matrices have entries. Previously I was referring to all three notions as “coefficients,” which is not wrong, but still less precise.
- Improved the art gallery example in the introduction. Instead of jumping straight to coordinates $(1,0)$ and $(0,1)$, I used arrow symbols like $\rightarrow$ and $\uparrow$ for the explanations in the introduction. This illustrates what is going on much better: the unknown linear transformation $T$ is a mapping from arrows-to-arrows. The coordinate transformations are not essential—they are just one way of representing the action of the linear transformation.
- Refactored the math fundamentals chapter to make it easier to follow for beginners. The material in Chapter 1 of the linear algebra book is shared with the No Bullshit Guide to Math & Physics, so all the recent improvements made in v5.4 of the math & physics book also appear in v2.2. update of the linear algebra book:
- Functions: I improved the explanations of functions’ input and output sets and their properties (injective, surjective, bijective).
- Completing the square: I added a much needed illustration of this important algebra procedure. Understanding this algebra trick and the geometric intuition behind it (Figure 1.15) is an essential “checkpoint” on every reader’s journey toward math proficiency.
- Linear equations: I added several figures (Figure 1.77, Figure 1.78) to illustrate the connection between the algebraic and geometric representations of linear equations. The algebraic equation $ax+by=c$ corresponds to a line in the Cartesian plane—the line consisting of all the coordinate pairs $(x,y)$ that satisfy this equation. Understanding this geometric interpretation of linear equations gives us another way to find solutions for systems of linear equations: the solution to a system of equations is where the lines meet (Figure 1.79, Figure 1.80, desmos:exikik615f). The geometry connection is useful for describing the special cases of no solutions when the lines are parallel (Figure 1.82) and infinite number of solutions when the lines overlap (Figure 1.83).
- Vectors: I added some explanations about the algebra rules for equations that combine points and vectors. I also added an example that motivates the importance of knowing the coordinate systems used to represent vectors.
- Notation: I stopped using the symbol ≡ (\equiv) which was confusing for many readers, and instead prefer the regular equality sign (=) and occasional use of the symbol ≝ in definitions.
- Fixes to problems P3.5b, P3.6c, P3.9a, P3.16, and P7.2, and exercises E4.5f and E7.5. See the book’s errata file for details.
For an exhaustive list of all the changes between v2.1 and v2.2 of the book, see this file diff_noBSLA_v21_v22.pdf (102 pages). The text shown in red has been removed, while the text shown in blue has been added.
As you can see in the above file, there were a lot of edits and improvements to the book. Based on reader’s questions and issue reports, I know which parts of the book need clarifications, and I implement those fixes to the source. I call this process “Kaizen for textbooks” (改善📚) and I plan to continue making such improvement and release updates v2.3, v2.4, etc. This is the power of print-on-demand publishing: if I update the print source files today, readers who purchase the book tomorrow will get the latest version printed for them.
If you purchased the book from gumroad, use the link you received by email to access the latest files. If you have a print copy of the book, you can send me a proof of purchase (e.g. picture or receipt email) to firstname.lastname@example.org and I’ll send you the the latest eBooks. There is probably no point in purchasing a new print copy for yourself, but you should consider buying a copy for a friend or family member who is interested in linear algebra (holiday season coming up, you know).
New readers can get the book in print or digital form from the following links:
- Softcover print from lulu: bit.ly/noBSLA-sc (this is the basic version for US$39 with consistent high quality printing).
- Hardcover print from lulu: bit.ly/noBSLA-hc (“deluxe” version for US$59).
- Softcover print from amazon: amzn.com/0992001021 (similar to the lulu softcover but sold by amazon so sometimes there are price discounts).
- Digital download from gumroad: gum.co/noBSLA (get the eBook and all future updates for US$29 if you don’t want to carry a physical book around).
In case you’re not familiar with the No Bullshit Guide to Linear Algebra, it’s a book that covers all the topics of linear algebra and also includes a review of prerequisites from high school math. The high school math review makes the material accessible for readers who have been out of school for a long time.
The book also includes hundreds of pages on the applications of linear algebra like balancing chemical equations, circuits, computer graphics, Fourier transformations, cryptography, error correcting codes, and even a chapter on quantum mechanics. Yes, that’s right—when you learn linear algebra a lot of new doors will open for you.
Check out the amazon reviews for the book to see what others are saying and check out the extended book preview (152 pages). You can also download a the concepts maps from the book: linear_algebra_concepts.pdf (3 pages).