Linear algebra done right

Linear algebra done right(linear.axler.net)

102 points by the-mitr 6 hours ago | 43 comments

wodenokoto 5 hours ago |

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...

_jcrossley 5 minutes ago | |

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.

[1] https://linear.mathcanbeahobby.com

dash2 4 hours ago | |

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.

aureate 4 hours ago | | |

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.

Tomte 4 hours ago | | |

Axler does limit itself to vector spaces over real and complex fields, though.

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.

mchinen 3 hours ago | |

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.

SpiralSource 1 hour ago | |

I strong second Strang. His book is the best first introduction to linear algebra, with "Done Right" marketing itself as a second course. Axler is notoriously shy with matrices, but Axler introduces them up front and uses them for the rest of the book.

geokon 3 hours ago | |

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)

pdhborges 2 hours ago | | |

Is this the book you are referring to? https://epubs.siam.org/doi/book/10.1137/1.9781611977448. It has 991 pages, not exactly what I would call concise.

ivankra 3 hours ago | |

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.

niksmather 3 hours ago | | |

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.

emil-lp 5 hours ago | |

+1 for Strang.

impossiblefork 4 hours ago | |

Lorenzo Sadun's Linear Algebra: The Decoupling Principle would probably be enough too if you added something about determinants.

qsort 4 hours ago | |

You zoomers are making a list of linear algebra books and not citing Lang? Get off my lawn ;)

porridgeraisin 1 hour ago | |

The nature of textbooks is that each one is better suited for a certain profile of reader. It depends a lot on the way the reader has learnt to learn things until that point in their life.

If you liked 3B1B's style, you will prefer strang over axler. Axler and treil to a greater extent focus on bringing out the abstract elegance and the kind of rigour a math major enjoys. Strang's book also has videos accompanying - on MIT OCW.

B&V VMLS on your list is interesting - they focus a lot on real-world instantiations of the concepts and have you code up things in the (excellent) exercises. Depending on your goals, you can do only this, or strang and then this. Definitely look at the exercises in any case though.

quailfarmer 4 hours ago | |

+1 for Boyd

emil-lp 5 hours ago |

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

h_mirin 4 hours ago | |

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.

hollowturtle 4 hours ago |

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

nayhel89 3 hours ago | |

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.

ivansavz 1 hour ago | | |

If anyone is interested, check out the PDF preview here https://minireference.com/static/excerpts/noBSLA_v2_preview....

and the printable concept maps here: https://minireference.com/static/conceptmaps/linear_algebra_...

n4r9 2 hours ago |

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.

[0] https://www.axler.net/DwD.html

ivansavz 1 hour ago |

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.

traes 1 hour ago |

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.

[0] https://www.axler.net/DwD.html

renyicircle 1 hour ago | |

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 whatever

inigyou 37 minutes ago | | |

Or "this one simple trick makes Big Linear Algebra hate you"

inigyou 38 minutes ago |

Human verification failed - so this is a broken link.

Bimos 4 hours ago |

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.

soVeryTired 1 hour ago | |

Yeah - otherwise it’s bizarre to have row vectors and column vectors.

Bimos 54 minutes ago | | |

To me it doesn't seem wrong to call covectors "row vectors", but one shouldn't simply convert them to each other with no good reason.

kopirgan 3 hours ago |

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..

Thanks!

dipanshuhappy 4 hours ago |

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.

dhruv3006 4 hours ago |

I passed the class just because of how good the book is.

LZ_Khan 3 hours ago |

i literally threw this book in the trash cause it was too dense and pretentious.

ouz-a 2 hours ago |

This is a holy book for a lot of game developers.

netfortius 4 hours ago |

Kindle format link == 404

contubernio 4 hours ago |

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.

qsort 3 hours ago | |

> 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.

traes 1 hour ago | | |

This polemic: Sheldon Axler -- Down With Determinants

https://www.axler.net/DwD.html

A strange and unpopular opinion.

nuclearnicer 3 hours ago | |

Something else you recommend?

lokimedes 3 hours ago |

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.

Rigor before Worth.

(Yes this is a pet peeve of mine :)

fithisux 4 hours ago |

These days, linear algebra done right should be accompanied with some CAS to view how algorithms are used.

Possibly paired with some numerical algebra free text (many on the Internet)

Tomte 4 hours ago |

Do not get the latest edition, the layout and typesetting is atrocious!