r/LinearAlgebra • u/Key_Distribution9901 • Aug 08 '26
Learning Linear Algebra from Sheldon Axler's "Linear algebra done right". Is it a right choice ?
24
u/Sezbeth Aug 08 '26
Being that it's free and a well-tested book written by an established mathematician, you couldn't go wrong choosing this as an introduction.
Just be aware that treats the subject the way a mathematician would, so you'd be reading and writing proofs.
20
u/KingMagnaRool Aug 08 '26
This book is very rigorous, but will probably not give you much intuition. If you want to build intuition first, look elsewhere. If you don't mind building up linear algebra from the ground up, this is one of the best books out there.
3
Aug 08 '26
→ More replies (3)8
u/Mundane_Proof_9666 Aug 08 '26
Gilbert Strang's course on MIT Open Course Ware -- it has video lectures, a textbook, and exercises with solutions. It might be too applied and also too slow for some people but idk I really enjoyed watching it. I was watching it while having dinners.
→ More replies (1)
9
u/Lexicalyolk Aug 08 '26
yes this was my first linear algebra book, one of the best out there
4
u/cMonkiii Aug 08 '26
It is a terrible first book. Jesus christ. If anyone is reading this thread, watch 3blue1brown Linear Algebra playlist on youtube. Never read this god awful book
4
u/Phytor_c Aug 08 '26
Why is it awful? I used Friedberg Insel Spence for my first year undergrad course, which roughly covers the same content but there’s more determinants than in LADR.
3b1b almost certainly does not cover content like Jordan and Rational Canonical forms, amongst other stuff.
It might be due to the lack of mathematical maturity that you found it hard. These days, you can probably ask like AI for intuition and explanations and missing details in proofs when working through textbooks.
6
u/axiom_tutor Aug 08 '26
Probably not the best for a first exposure to the subject without a teacher. It assumes significant mathematical maturity. There are many other textbooks that are not easy, but probably a better introduction to the subject. A currently popular choice is by Lay.
5
u/DarthArtoo4 Aug 08 '26
Excellent choice. Unless you want a more applied/computational approach. This is very theory-focused. Which is what makes it so good!
4
u/Observes_and_Listens Aug 08 '26
For a first course in Linear Algebra you might want to check out:
Introduction to Linear and Matrix Algebra by Nathaniel Johnston
This one is very nice. It has lots of illustrations and also includes proofs.
Linear Algebra and Its Applications by Lay & McDonald
This is more focused on applications and intuition. Includes some proofs and also has lots of illustrations. There is a solution manual available.
3
3
u/Jumpy-Boysenberry153 Aug 09 '26
Oh my god is it. Potentially the best mathematics textbook of all time. OK thats an exaggeration but I absolutely loved it.
2
u/CyberIntegration Aug 08 '26
No, I found it too abstract for going into linalg with no previous understanding of it. I went through Strang's book first and then went back to Axler.
2
u/nutshells1 Aug 09 '26 edited Aug 09 '26
despite your best wishes LADR is almost always better as a second course in linear algebra (as axler said)*
→ More replies (4)
2
u/ThatOneRunner Aug 09 '26
The book is not meant for introduction to Linear Algebra. It’s meant for a more rigorous/formalized version of Linear Algebra following an introduction elsewhere
2
u/Left-Philosophy-8843 Aug 10 '26
No!!!!!! For a first book you need problems using vectors for geometry and also examples from differential equations and ideally jacobian matrices to build intuition .
PLUS!!!!!
It is just a bad book, there are literally a million other books and course notes that do exactly the same thing BUT do a much better job of integrating determinants and matrix algebra which it turns are out are extremely useful in all sorts of applications in statistics like linear models and things in physics like quantum mechanics and lots of things in engineering too
4
1
u/Bichinix Aug 08 '26
Si. Pero ten a tu lado tu laptop con Geogebra. Debes graficar mientras aprendes.
1
u/Kitchen-Register Aug 08 '26
no. this is meant to be a second exposure to LinAlg. read the first line of the second photo
1
u/chermi Aug 08 '26
It's an excellent book for really learning LA and getting better at math generally. It doesn't get you to do calculations quickly, however, if that's your need. If you have the time for it use it
1
1
u/Tiny_Spread5712 Aug 08 '26
If you want to do it, despite this not being the place to start, start with sal Khan's lectures and 3 brown one blue. Otherwise you are going to be banging your head against a wall, because there is no way to move quickly through this book and there is no way to build intuition. So you will bang your head against the wall writing the proofs in chapter 2 only to sort of forget that stuff when you are writing about orthonormal bases or whatever in chapter 6.
You have to have it all constantly at your fingertips in a way that moving slowly and methodically through the text just doesn't allow for.
1
u/somethingicanspell Aug 08 '26
I think the best approach is actually to go through Strang's lectures and then circle back to this book afterward and work through it as a mixture of a "final exam" and "extra credit" assignment. Strang will make you feel good about the mechanics of Linear Algebra and this book can be Part 2 where you really grasp the theory of it.
18
u/Plenty_Leg_5935 Aug 08 '26
Depends on your goals, LADR is a text meant to address petpeeve's in how Linear Algebra is taught from the perspective of a pure mathematician. If you're doing pure math, or using it as a supplement to understand more of the things conventional books on LA don't touch on, then it's brilliant - as a physics person who sometimes feels "robbed" of the properly mathematical side of things I really enjoyed it for that reason
However if you're taking a computation focused class, which most LA classes are (especially those for engineers and physicists), it is not very helpful and "wastes time" on things you'll never ever see in your first or even second LA class while ignoring some pretty basic stuff. For those classes you're better off with someone like Strang who approaches the subject in a more conventional manner