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- Hacker News
- 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.by contubernio
- Something else you recommend?by nuclearnicer
- > 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.
by qsort - I got halfway though the exercises with the help of a reading group. They were very hard, bit thought provoking, so I would definitely recommend. Don't feel discouraged if you get stuck and try not to look at the solutions right away.by ivansavz
- In the 1980s, being not entirely adept at mathematics I recall scouring every library and bookstore I could find for any snippet that would explain a proof, or even a concept, so that I could understand it. Videotaped lectures by other professors were sometimes available on campus too.
On a daytime episode of David Letterman, Isaac Asimov predicted fiber optics would one day bring about television studios in people's homes: https://youtu.be/cIB1b_8hqB0?si=212sGzZ71VIZORML&t=696
All sources of understanding are so very much appreciated.
by nstents - Check out page 196 for a Shakespearean style sonnet on the Cauchy-Schwartz inequality, courtesy of Chat-GPT.
- 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.
- 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 easilyby hollowturtle
- 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.by nayhel89
- 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
- Absolutely love Dr. Grinfeld! I watched some of his differential geometry series and his explanations are very accessible!by ksd482
- 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 https://news.ycombinator.com/item?id=41416799
by emil-lp - Previously in my ~/Downloads:
linear_algebra_done_right.pdf, 0 pages read, July 2023
linear_algebra_done_right (1).pdf, 0 pages read, Oct 2023
linear_algebra_done_right (2).pdf, 0 pages read, Sept 2024
Downloading (3) now.
by h_mirin - 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.by n4r9
- 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.by traes
- Maybe you need to speak to better math professors.by tanderson92
- Yeah I feel like this "done right" part is responsible for most of the popularity of this book. Makes the reader think they've been learning it wrong. Kind of like these clickbait videos "you've been folding your laundry wrong your whole life!" or whateverby renyicircle
- Determinants are easy to use but very hardly to grasp intuitively, this is not a minority point of view. See countless of StackOverflow questions begging for a conceptual exposition of determinants.
The easiest conceptual handle is geometric: volume expansion, but seeing how this is related to the combinatorial sum over all permutations, or how those two point of views are related to the algebraic one (that a set of equations having a solution or not), is not easy to see even in the 2D case.
I won't be surprised if math professors don't have this issue like you said (especially if someone is comfortable with wedge products), but the vast majority of newcomers who are interested in understanding why something works rather than just how to use it struggle all the time with determinants.
by ak_111 - If you want to dive deeper into applications, refer to Linear Algebra and Geometry by I. Kostrikin, Yu I Manin.
This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metic, the theory of Hilbert polynomials, and projective and affine geometries. Unusual in its extensive use of applications in physics to clarify each topic, this comprehensice volume should be of particular interest to advanced undergraduates and graduates in mathematics and physics, and to lecturers in linear and multilinear algebra, linear programming and quantum mechanics.
by sfilkin - 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...
by wodenokoto - "Linear Algebra and Its Applications" by David Lay is the best introductory linear algebra textbook, hands down. Love it.
- LADW saved me in undergrad, but I was pretty much exactly the target audience in an honors-level freshman math course:
"[per Treil, LADW is for] a student who, while not yet very familiar with abstract reasoning, is willing to study more rigorous mathematics than what is presented in a “cookbook style” calculus type course."
But yeah it's really attempting to introduce you to higher mathematics rather than get you comfortable doing linear algebra per se.
by c_moscardi - 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.by dash2
- Strang's lecture series are a nice and friendly accompaniment, especially if you don't have a reading group https://www.youtube.com/watch?v=7UJ4CFRGd-U&list=PL221E2BBF1...
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.
by mchinen - I first learned from self studying Finkbeiner’s “Introduction to Linear Transformations and Matrices” which I thought was very good. Great exercise's. Dover still prints it for pretty cheap. He does a cool thing introducing all sorts of theory of linear transformations, then later showing that matrices are the way to encode them once you chose basis for domain and codomain. I liked that a lot, felt like it removed any magic from matrices. Also a fan of Axler though.by tpdly
- I found Linear Algebra by Friedberg, Insel and Spence to be excellent. Very clear, modern notation, great exercises. It's also what Tao lectured from in 115A: https://www.math.ucla.edu/~tao/resource/general/115a.3.02f/by laichzeit0
- The thing about linear algebra is that it isn't really a cohesive subject in the same way that calc is. This is why you get as many perspectives as you get commenters.
There are some central concepts, and which ones matter to you depends on what you're planning to do with your future. The key points are:
* Matrices/vectors as grids of numbers/computational tools.
* Matrices/vectors as positions and transformations of those positions.
* Matrices/vectors as more abstract geometric objects
* Matrices/vectors as algebraic objects.
There is no 'done right' imo. My sense is LADW is probably the best option for a motivated honors math student, because unlike Axler the author doesn't hate determinants for whatever reason. Strang would work well for engineers. Axler is mostly concerned with the last two, but IMO this makes him kinda niche.
by thelaxiankey - As a math educator, I strongly dislike both Strang and Axler for a 1st course. I've heard great things about Strang's lectures, but his book is disorganized and too heavy on computation. Axler's book is wonderful, but as explicitly stated on the back cover, it's designed for a 2nd course and primarily aimed at math majors.
I recommend and teach my YouTube Live series out of Fraleigh [1], but unfortunately it's out of print. Lay seems to be a good modern alternative.
by _jcrossley