Linear Algebra
"The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Each chapter has three or four discussions of additional topics and applications. These are suitable for independent study or small group work."--Page 4 of cover
Stats for nerds
7recommend
16mentions
12people
2011–2026years
63% recommend38% neutral
Mentions per year
What Hacker News says
- Linear Algebra by Jim Hefferon can be read online for free.
- I found the book "Linear Algebra" and accompanying lecture recordings by Jim Hefferon very approachable and solid.
It's free, including exercises and an (also free) solutions book.
- (Math professor here)
What do you mean by "foundational"?
I love Calculus Made Easy, but in my opinion the reason it's so good is that it doesn't try to be foundational. It relies on quick and dirty tricks -- especially, treating dy/dx as a fraction when it can't be formally defined as such, but where doing so makes the subject much more intuitive and easy. It's not really a good foundation for further study, you need something that doesn't cut corners for that, but it's fantastic for what it is!
My favorite foundational book is Linear Algebra by Jim Hefferon:
https://hefferon.net/linearalgebra/
It is free, and I've seen the author on HN occasionally. It's foundational in the sense that it builds up the subject brick by brick, assuming the minimum realistic prerequisites needed, and it does an outstanding job of this.
But it's a slow read, essentially by design. If you want something quicker, you might try Interactive Linear Algebra by Margalit and Rabinoff:
https://textbooks.math.gatech.edu/ila/
Again free, with lots of widgets to play with.
Some other textbooks I really like:
Epp's Discrete Mathematics is fantastic. The newest edition is astronomically expensive, so go looking for used copies of previous editions.
Carter's Visual Group Theory is tremendous fun. Once again not foundational per se, but if you want to learn what group theory is all about without slogging through lots of formalities, that's a great choice. I'd say that roughly it's in the spirit of Calculus Made Easy.
Also, if you enjoy poker, check out Dan Harrington's books on the subject. In the course of explaining hold'em strategy, they will teach you lots about probability, counting, expected value, and game theory in an applied setting. They're fantastically written.
- I have recently been using the Linear Algebra book by Jim Hefferon to study the subject. This is because I'm taking a linear algebra course in college, I am visually impaired, and the books I get from college are literally unusable.
As a person who has to use a Screen Reader, math in PDFs is almost impossible to read for me. The problem is almost insurmountable if the PDF is a collection of images, but even if it is a LaTeX-generated PDF, reading anything but the simplest of equations is very, very hard. In these cases, having the LaTeX source to read is a godsend.
To the authors who publish the source of their books: thank you, thank you. I cannot express how grateful I am. To anyone who is related to /working in the publisher space: it would be incredibly useful if there was a process to get the LaTeX source of books upon request, although I understand how copyrights/etc might make this difficult.
Some other books I would like to point out for being open source: Apex Calculus, Open Data Structures.
- I found that even Introduction to Statistical Learning made a few too many assumptions when I tried to work through it. I recently finished Jim Hefferon's Linear Algebra [1] and now I'm working through Introduction to Applications of Linear Algebra: Vectors, Matrices, and Least Squares [2] (along with a python companion [3]). The two texts have overlaps but I've found them more helpful than redundant; it's nice to hear different angles on the same topic. I'm planning to focus on statistics next with Blitzstein and Hwang's Introduction to Probability [4] before returning to ISLR.
[1] http://joshua.smcvt.edu/linearalgebra/
[2] http://vmls-book.stanford.edu/
- Jim Hefferon, who is also a HN member, has a great free Linear Algebra textbook. People all have their own preferences but I actually prefer his to Strang's.
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