This is supposedly based on Sheldon Axler's earlier and shorter paper "Down With Determinants!" [0]. I lectured mathematics for a while at a "former polytechnic" and used to enjoy leaving print-outs of this sort of paper in the faculty communal areas.
Strang is simpler and clearer. Axler is more advanced in the sense that it doesn’t tie it to matrices. Strange is a “first course” book, Axler is a second course.
Depends how you think. I found Strang impenetrable and Axler simple and lucid. Some people seem to find abstract vector spaces weird and unmotivated without doing a load of stuff with lists and grids of numbers first. I find determinants weird and unmotivated without learning exterior algebra first. I wish Axler had been my first course.
I really recommend Matrix Analysis and Applied Linear Algebra by Carl Meyer. It's both concise and comprehensive. Strange is very good, but feels kinda vague and long winded in comparison (very good for a high level understanding of the tools you're dealing with)
If you liked 3B1B and prefer intuition/applications-heavy view, then definitely Strang over Axler. Check out especially his newer textbook "Linear Algebra and Learning from Data".
Axler is more of a pure math textbook - if you want to dive more into proofs and abstractions.
I would also say Axler is much better prep for higher level applied math, as well as pure. If you are interested in how the big ideas of linear algebra extend to things like Fourier analysis it's very helpful to see the more abstract explanation of vector spaces.
For those who find Linear Algebra Done Right too much to start with, and those who don't get why Strang starts with matrices, I can't recommend more "The dark art of linear algebra" read this first. With this you can then tackle every other book on the topic more easily
My personal favorite is No Bullshit Guide to Linear Algebra - it gives a really good overview of math fundamentals and overall strikes a good balance between keeping things simple and giving enough insight to comfortably dig deeper in the topic.
I found it really insightful (and always overlooked) to distinguish between vector and co-vector spaces. It doesn't necessarily produce new knowledge, but makes things more clear.
I wanted to learn the underlying principles of LLM/AI and got myself Shilov's book. Wow that was so thick, each paragraph took a while to figure. This could be a nice option..
Overrated and tendentious book. There are many better linear algebra texts. His polemic against determinants is poorly motivated, misguided, and distracting. The writing is quite formal and not terribly inspiring. The coverage is adequate but nothing more.
> His polemic against determinants is poorly motivated, misguided, and distracting.
What polemic? Defining the determinant as the unique multilinear alternating form satisfying certain properties is very normal (and in fact the only way that really makes sense for both finite- and infinite-dimensional vector spaces). There are zero unusual things with this book imo.
Lately been deep diving into linear algebra. And a way which i engage with it is that I tell AI to generate interactive examples + questions on Lean or Haskell. Its so fun, just deriving the intuition in these languages.
My bag of tricks is better than your bag of tricks. Alright.
As with most textbooks, it fails to motivate why reading it is worth the investment.
Perhaps it is a millennial old tradition of the Greek mystery schools, that the rite of passage came by proving your commitment to material knowledge without anything but fate in the school itself as motivation.
[0] https://www.axler.net/DwD.html
The contenders seems to be:
- Linear Algebra Done Right - Sheldon Axler
- Liner Algebra Done Wrong - Sergei Treil
- Introduction to Linea Algebra - Gilbert Strang
- Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares by Stephen Boyd and Lieven Vandenberghe
[1] https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x...
LADW and LADR are great too, for an honors approach with more focus on proofs. To me it would make more sense on a second pass.
That‘s fine, but I would have appreciated notices, which proofs and theorems do not hold in the general case.
It‘s an exercise for the reader.
Axler is more of a pure math textbook - if you want to dive more into proofs and abstractions.
Linear Algebra Done Right 58 points, July 2023, 4 comments https://news.ycombinator.com/item?id=36576114
Linear Algebra Done Right – 4th Edition, 631 points, Oct 2023, 294 comments https://news.ycombinator.com/item?id=38060159
Linear Algebra Done Right [pdf], 85 points, Sept 2024, 39 comments https://news.ycombinator.com/item?id=41416799
linear_algebra_done_right.pdf, 0 pages read, July 2023
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Thanks!
What polemic? Defining the determinant as the unique multilinear alternating form satisfying certain properties is very normal (and in fact the only way that really makes sense for both finite- and infinite-dimensional vector spaces). There are zero unusual things with this book imo.
As with most textbooks, it fails to motivate why reading it is worth the investment. Perhaps it is a millennial old tradition of the Greek mystery schools, that the rite of passage came by proving your commitment to material knowledge without anything but fate in the school itself as motivation.
Rigor before Worth.
(Yes this is a pet peeve of mine :)
Possibly paired with some numerical algebra free text (many on the Internet)