Introduction to linear algebra
Book Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.
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37recommend
62mentions
58people
2007–2026years
61% recommend32% neutral6% critical
Mentions per year
What Hacker News says
- I'd recommend Gilbert Strang's Introduction to Linear Algebra and 3B1B's calculus and linear algebra series. They focus on the intuition part of math, which makes it fun and interesting. After that do some problem sets, that should give you a solid foundation to understand ML papers with the help of things like ChatGPT.
- I have this book. It's been more than great. I fully recommend it to anyone looking for a quick and simple introduction to linear algebra
- Gilbert Strang's "Introduction to Linear Algebra" made it all click for me. I read it at the beginning of PhD studies and in a few weeks it all made more sense than during all of my Master's studies before.
Coincidentally to this question, he will live stream his final lecture on Monday: https://grinfeld.org/strang/
I was amazed reading that, as I wasn't aware he even lectured anymore. And after googling a bit and finding out he is already 88 years old, I was even more amazed. What an amazing human being, probably many thousands of people in the sciences and engineering owe quite a bit to his life's work.
- Off the cuff, here are a couple of textbooks not yet mentioned elsewhere on this page (so far):
* "An Introduction to Statistical Learning" by James, Witte, Hastie, and Tibshirani: possibly the best intro to the topic I've seen.
* "Introduction to Linear Algebra" by Gilbert Strang: possibly the best intro to the topic I've seen.
Also, here are some books that are not properly textbooks but could be used as such:
* "Robot: Mere Machine to Transcendent Mind" by Hans Moravec: remarkably prescient, in hindsight.
* "On the Origin of Species" by Charles Darwin: I was surprised at how readable it is.
* "The Selfish Gene" by Richard Dawkins: It made me question a lot about a lot.
* "The Better Angels of Our Nature" by Steven Pinker: I was shocked at the violence in our past.
* "Gödel, Escher, Bach" by Doug Hofstadter: an intellectual tour de force.
- Strang's "Introduction to Linear Algebra". This book is a friend!
Garrity's "All the Math You Missed". Brings you up to speed fast, and has great references.
- My initial goal was to understand mathematics well enough to have a some grasp of "Deep Learning" (2016) textbook by Goodfellow, Bengio, and Courville. I meant like 50-85% understanding of the math depending on the chapter. And being able to have reasonable understanding of deep learning papers being published in the 2012-2018 period. https://www.deeplearningbook.org
1. Because my math was pretty rusty, I started with single-variable calculus. Good resources for this are Khan Academy including pre-calc prequisites all the way up to multivariable calc and linear algebra. I'm not sure which textbook on single-variable calc is good but there are many many to choose from.
2. For multivariable calc, I began with Lang's "Calculus of Several Variables". https://link.springer.com/book/10.1007/978-1-4612-1068-9
3. After Lang, I did a lot of the problems in the first half (differentiation only) of Baxandall and Liebeck's "Vector Calculus". This is truly an outstanding book; such clear exposition and excellent organization with many examples. It was a little more formal in it's presentation than I was used to. But this helped me learn to write decent and well-organized proofs. And when I got to item 6 below, Baxandall and Liebeck got me ready! https://store.doverpublications.com/0486466205.html
4. In parallel, I studied linear algebra. My two main intro books were Strang's "Introduction to Linear Algebra" (4th edition). https://math.mit.edu/~gs/linearalgebra/
But I found Strang (super popular among college students) was well-supplemented by Kuldeep Singh's "Linear Algebra Step-by-Step" https://global.oup.com/academic/product/linear-algebra-97801...?
5. At this point, the Khan Academy videos on linear algebra were very helpful.
6. Now that I was ready, I started Axler's "Linear Algebra Done Right". It's more formal and abstract compared to 4 and 5 above. I love it though! It's taken me years and I'm still only part way through. It is one of my all-time favorite books--not just in math--but in any field. I'm a bit slow at this type of abstract / proof-based math but it's deeply deeply satisfying. https://linear.axler.net
7. Recently, I started Jacobson's "Basic Algebra I". I'm only at the beginning of my journey into modern algebra but I really like it so far.https://www.maa.org/publications/maa-reviews/basic-algebra-i...
Hope this helps!
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