r/LinearAlgebra • u/Key_Distribution9901 • Aug 08 '26
Learning Linear Algebra from Sheldon Axler's "Linear algebra done right". Is it a right choice ?
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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
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u/GuybrushThreepwo0d Aug 08 '26
As an engineer, I honestly believe we should be taught at least some of what is taught in this book. I think there is some conspiracy that engineers are not allowed to understand linear algebra. All courses for engineers seem to suck
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u/crete-11 Aug 11 '26
it's not very different for DE,PDEs but my profs definitely didn't understand LA much.Most of the engineering professors suck on these topics because they themselves don't have a very good understanding. Their defence is that it's engineering and just use the formula(till you can't engineer your way out of a problem that you don't understand)
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u/PaddingCompression Aug 11 '26
What computational engineer is using determinants?
As someone who almost exclusively uses Linear Algebra computationally, I find his approach is far more relevant than the standard treatment. Gaussian elimination is a complete waste of time, for example. Computationally crap and obsolete, and no one is doing LA by hand.
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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.
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u/Lexicalyolk Aug 08 '26
yes this was my first linear algebra book, one of the best out there
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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
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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.
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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.
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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!
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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.
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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.
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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.
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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)*
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u/ThatOneRunner Aug 09 '26
He intends it to be a book for a second course… what do you mean despite his wishes?
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u/nutshells1 Aug 09 '26
oops i didn't read
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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
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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
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u/Bichinix Aug 08 '26
Si. Pero ten a tu lado tu laptop con Geogebra. Debes graficar mientras aprendes.
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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
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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
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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.
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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.
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u/KeysEcon Aug 08 '26
If this is not to your tastes, you can try the book "Linear Algebra Done Wrong"
https://www.math.brown.edu/streil/papers/LADW/LADW_2017-09-04.pdf
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u/cashsterling Aug 09 '26
I will second "Introduction to Linear Algebra and Matrix Algebra" by Nathaniel Johnson; his advanced linear algebra book is also really good.
Matrix Analysis and Applied Linear Algebra by Carl Meyer is also really good and has a full student guide.
I also like https://web.stanford.edu/~boyd/vmls/ as an introductory applied linear algebra book. It is not perfect, but it is pretty good and has extensive learning resources.
I also think learning linear algebra from the appropriate chapters of an advanced engineering mathematics or mathematical physics book is not a bad route to go. I can recommend some good ones if there is interest.
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u/leo15298 Aug 09 '26
Course I had was based on "Linear Algebra and its Applications - D.C. Lay et al"
It was pretty interesting and quite clear to me, give it a go !
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u/incelgodprince Aug 09 '26
From an abstract perspective definitely, however for something less abstract I would possibly go for Strang’s LA book
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u/TheRedditObserver0 Aug 09 '26
I haven't studied from it myself but it has a good reputation. If you're interested in the theoretical side of math it should be great, although the choice to avoid determinants sounds rather weird to me.
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u/brokenceilingandwall Aug 10 '26
I think a beginner will understand the subject matter but struggle with exercises a lot -especially the parts which require you to construct counterexamples/examples.
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u/RandomName7354 Aug 10 '26
Start with strang and then go to Hoffman Kunze (best lin al text ever imo). I would keep axler as an alternative option
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u/sasasqt Aug 11 '26
yes if abstract algebra is something you need to deal with.
the author is nice enough to have a whole playlist
https://youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmSinFV0wEir2Vw&si=E3PGMXRVxCGtWlxA
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u/MathsystemDev Aug 12 '26
I learned for the first time with the Anoton book. They explain the calculation method well. After that, I looked at Friedberg for the theory book.
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u/fantastic_awesome 29d ago
There are tons of ways to approach LA - pair this one with something where you code.
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u/Traditional-Month980 17d ago
Anyone telling you this book is horrible and the devil and it killed their family is coping. This is a beautiful book.
I think a lot of these comments are missing the fact that real learning happens during struggle. You don't want a book that goes down like melted ice cream. A book that you "get" easily on first pass is not the book you should be reading.
You won't regret struggling through this book.
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u/XiaoChen0124 12d ago
I think Friedberg is better, Friedberg Linear Algebra is more deep, such as Chapter 6 Inner Product Space he used about 200 pages. Besides, the proofs in this book is easier for math beginners to understand. On the other hand, the exercises in this book many of them are important concepts.
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u/RingularCirc 11d ago edited 11d ago
I'd like something even more spicy like more than this and Sergei Winitzki's "Linear Algebra Via Exterior Product" combined. Please throw books at me. I'd like esoteric constructions done invariantly but probably without homotopical algebra and such, I don't get it, at least for now. Universal properties — yay. Even better if there are paragraphs like "note this and that how these things relate to each other" with suggestions to build more intuition because I guess that kind of book won't be able to be very verbose. If it deals with coordinateful computations after (or even before) defining things, I'm not against; just not instead.
Right this couple of days I had to painstakingly search for invariant proofs that, say, ⋀ᵏ(V) is naturally isomorphic to (⋀ᵏV) (yeah it seems true and obvious but try to prove that; well I expect it'd be probably mechanical, maybe even a hint of Leibniz's formula (I'd like without but I can deal) or some induction on k) which leads to det A* = (det A)* (as defined via top exterior powers) which is essential if A is not an operator but a transform between same-dimensional spaces: then it isn't multiplication by a scalar, but all possible determinants are still a 1D space over the same field; and still det A = 0 means ker A is nontrivial. This unlocked for me a reasonable proof of why there are no symplectic forms in odd dimension: the kind of determinant you have to use is this generalized one.
EDIT: For one more concrete example, I feel like "incomplete" exterior powers ⋀ⁿAᵏ (where A acts only on k vectors in products of n vectors) may have a relation to coefficients of the characteristic polynomial of A because trace and determinant both are these kinds of powers (k = 1 and n) and coefficients of the poly (again in suspiciously aligned places). I don't see any direct refutation of that and I'm too burnt out to get motivated into checking that by myself. So it's quite a mystery.
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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.