Linear Algebra Done Right: A Determinant-Free Masterpiece
Linear Algebra Done Right – Sheldon Axler
Sheldon Axler's fourth edition of Linear Algebra Done Right is now open access in English, Chinese, Farsi, Greek, and Portuguese. The book famously banishes determinants to the end, focusing on the structure of linear operators. This edition adds over 250 new exercises and 70 new examples. It's a best-selling textbook for a second course in linear algebra, praised as a 'didactic masterpiece' and 'the most original linear algebra book to appear in years.'
To so consistently do without determinants constitutes a tour de force in the service of simplicity and clarity.
- wodenokoto
Last night I was looking into what to read after or along with 3Blue1Brown's series of Linear algebra videos [1]
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...
- traes
Note that "done right" means done with Axler's completely subjective and unusual hatred of determinants, chronicled here [0]. It is in no way "done right" in some definitive, rigorous way; most math professors I have spoken to either strongly disagree with the presentation or have no particular preference.
- n4r9
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.
- emil-lp
Previously on Hacker News:
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
- penguin_booze
When it's described in plain English [0], with lots and lots of examples, that's when I call it done right.
This is the best I know: https://www.youtube.com/watch?v=Fnfh8jNqBlg&list=PLlXfTHzgMR....
[0] I meant natural language
- throwaway902984
In a computer science context, I have to plug the old FLAME group for publishing and teaching the topic so well. - digging into parallelizing computations efficiently before neural nets took off around the 2014 time.
LibFlame has long been abandoned now but their courses were very strong when you had access to the professors. They have been rebranded as the Science of High Performance Computing (SHPC) group.
- hollowturtle
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
- maxwell_smart
Check out page 196 for a Shakespearean style sonnet on the Cauchy-Schwartz inequality, courtesy of Chat-GPT.