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Anonymous Tue 10 Dec 04:52:59 2019 No.11214242 View Reply Original Report

Quoted By: >>11214249 >>11214312 >>11214348 >>11214405 >>11214415 >>11214418 >>11214425 >>11214543 >>11214836 >>11214958 >>11215742 >>11216582 >>11216843 >>11217713 >>11217718

Why does half of the math community hate this book while the other half love it?

Just take a look at this vids comments and on some threads here. It's the most divisive book in mathematics right now.

https://youtu.be/m79WBNHXc58

Anonymous

Anonymous Tue 10 Dec 2019 04:56:30 No.11214249 Report

Quoted By: >>11214257 >>11216085

>>11214242
>Why does half of the math community hate this book while the other half love it?
Because half the math community is too retarded for determinants

Anonymous

Anonymous Tue 10 Dec 2019 05:00:48 No.11214257 Report

Quoted By: >>11214394

>>11214249
Aren't you being a little too restrictive when you summarize the whole field of Linear Algebra to only determinants? How many LA books do we have that usea determinants from the start? Hundreds? Thousands? Why does a book that choses to make things differently, to give an elegant view of LA that doesn't rely on a cheap method deserve so much hate? Because it's simply different? Open up your narrow conservative mind a little bit and maybe you'll become a little more successful mathematician rather than a /sci/ poster.

Anonymous

Anonymous Tue 10 Dec 2019 05:30:39 No.11214312 Report

Quoted By:

>>11214242
It's title is supremely arrogant and dismissive

Anonymous

Anonymous Tue 10 Dec 2019 05:46:33 No.11214348 Report

Quoted By: >>11214369

>>11214242

how is this book different from every other linear algebra book?

Anonymous

Anonymous Tue 10 Dec 2019 05:55:17 No.11214369 Report

Quoted By: >>11214418 >>11214872 >>11215913

>>11214348
It builds the entirety of Linear Algebra without using determinants a single time.

Anonymous

Anonymous Tue 10 Dec 2019 06:02:06 No.11214394 Report

Quoted By:

>>11214257
>to give an elegant view of LA
There's nothing "elegant" about building a subject while arbitrarily disregarding an extremely useful tool

Anonymous

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Anonymous Tue 10 Dec 2019 06:07:18 No.11214405 Report

Quoted By: >>11214418

>>11214242
Determinants are based, Axler is a pleb.

Anonymous

Anonymous Tue 10 Dec 2019 06:14:31 No.11214415 Report

Quoted By: >>11214808 >>11215749

>>11214242
It's good for engineers and applied mathematicians.
It's useless for pure maths.
I appreciate it but I hate the zealous fandom of the book that treats it like panacea. For a pure math course it is just a waste of time. But again, great for applied maths.

Anonymous

Anonymous Tue 10 Dec 2019 06:16:47 No.11214418 Report

Quoted By:

>>11214242
Axnerd should be beaten, tarred and feathered
>>11214369
>It builds the entirety of Linear Algebra without using determinants a single time.
It's also possible to dig a trench with a spoon
>>11214405
Shilov had sex way more often than Axler, you can just tell

Anonymous

Anonymous Tue 10 Dec 2019 06:20:37 No.11214425 Report

Quoted By:

>>11214242
Ironic title

Anonymous

Anonymous Tue 10 Dec 2019 06:22:24 No.11214427 Report

Quoted By:

Axler is a meme.

Anonymous

Anonymous Tue 10 Dec 2019 07:56:12 No.11214543 Report

Quoted By: >>11216503

>>11214242
its a good book but i know the reason its hated after first loving it and now Im not that big of a fan. Its about the format of it. The colours and all that other highschool textbook crap makes it unreadable, especially after going through so many latex black and white books, ive grown to love the simplicity and elegance in no colour or godawful headings/highlightings of defs,theorems,etc.

Anonymous

Anonymous Tue 10 Dec 2019 07:57:14 No.11214546 Report

Quoted By:

also I hear lin alg done wrong is a better one written by a ruski

Anonymous

Anonymous Tue 10 Dec 2019 13:05:39 No.11214808 Report

Quoted By: >>11215059

>>11214415
Spoke like someone who didn't even touch the book. There's nothing applied or computational in it, it's entirely proof based, what a fool you just made of yourself right now...

Anonymous

Anonymous Tue 10 Dec 2019 13:40:33 No.11214836 Report

Quoted By:

>>11214242
why does anyone care? nearly anyone who has the spare time to read this book is probably AT LEAST a good student, and probably learned something interesting about formulating linear algebra in a nonstandard way.

Anonymous

Anonymous Tue 10 Dec 2019 14:07:15 No.11214872 Report

Quoted By: >>11214885

>>11214369

how is that better than using determinants?

Anonymous

Anonymous Tue 10 Dec 2019 14:17:43 No.11214885 Report

Quoted By: >>11214948 >>11215431

>>11214872
its not supposed to be "better", retard

Anonymous

Anonymous Tue 10 Dec 2019 15:06:25 No.11214948 Report

Quoted By: >>11214989

>>11214885

then what's the point?

Anonymous

Anonymous Tue 10 Dec 2019 15:12:53 No.11214958 Report

Quoted By:

>>11214242
I think it does some things very well, but eschewing the use of determinants to THIS degree is somewhat silly imo. In any case, it's a well-written book very much unlike the others of the field, so it's interesting to read at least once, even if only for fun.

Anonymous

Anonymous Tue 10 Dec 2019 15:41:46 No.11214989 Report

Quoted By:

>>11214948
To show things in another perspective, mathematics is not a one-way path, but several with several ways.

Anonymous

Anonymous Tue 10 Dec 2019 16:29:55 No.11215059 Report

Quoted By: >>11215109 >>11215110 >>11215182 >>11215435

>>11214808
I agree with him, a book on linear algebra that doesn't even mention exterior forms is useless to a pure mathematician. If, as you claim, it is not for applications, then the point of the book eludes me - what is the intended audience?

Anonymous

Anonymous Tue 10 Dec 2019 17:04:13 No.11215109 Report

Quoted By:

>>11215059
>exterior forms
literally not linear algebra
>what is the intended audience?
1st or second semester students of linear algebra

Anonymous

Anonymous Tue 10 Dec 2019 17:04:13 No.11215110 Report

Quoted By: >>11216896

>>11215059
>I agree with him
Heh, are you agreeing with yourself then? You think you're fooling anyone speaking like a different person? Let me tell you this boy, the entire exercises on the fucking book are proof-based, there are proofs for every theorem, it's used in graduate courses in some universities, but oh no the kiddo who didn't even touch the book is saying it's a book for engineers and applied mathematicians because there's no exterior forms buah buah, what a joke.

Anonymous

Anonymous Tue 10 Dec 2019 17:30:41 No.11215149 Report

Quoted By:

People are way to dramatic over textbooks. It is a decent book for introduction linear algebra with proofs. I have graded for course that used it, the examples are illustrative. The exercises have a good mix of easy to reinforce the definitions and theorems to somewhat involved interesting applications. Axler is just a douche for calling "done right" as if using determinants are doing it wrong.

Anonymous

Anonymous Tue 10 Dec 2019 17:48:19 No.11215182 Report

Quoted By: >>11215253

>>11215059
>I agree with him, a book on linear algebra that doesn't even mention exterior forms is useless to a pure mathematician
?
which undergraduate level, introductory linear algebra text actively uses exterior forms? and don't say Hoffman&Kunze because it's just one short isolated chapter that they specify you can skip if you want to. only other I can think of is an independent text, available online, called literally "Linear Algebra via Exterior Products" and its whole approach is to ditch coordinate based LA, which isn't exactly mainstream at the undergraduate level.

Anonymous

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Anonymous Tue 10 Dec 2019 18:37:54 No.11215253 Report

Quoted By: >>11215426 >>11216834

>>11215182
?y???pe?, ?a??o? - ???e??a? A??e?pa ? ?y????? ??o??? ?epe?e????

I don't care if you dismiss it because it's not in English. I was personally taught linear algebra through this text when I was a first-year first-semester undergraduate. The text properly introduces the determinant in the only mathematically correct way (pic related).

You live in your bubble with shitty textbooks that give engineer-tier explanations and genuinely think it is sufficient for a pure mathematician? Pretty laughable.

If you don't learn it the proper way the first time, when are you supposed to, then? Second year is already differential geometry, de Rham cohomology, Poincare duality, Mayer-Vietoris, Thom classes, etc., and it's just a waste of time to relearn linear algebra, nobody does that when designing a pure maths course (at least here in Russia).

I chimed in just because someone mentioned pure maths. Maybe the OP book is good for others, I can't say, I only said what I was sure about - a proper pure math course has no time for 12 different linear algebra courses, and the OP book is a bad book from this perspective.

Anonymous

Anonymous Tue 10 Dec 2019 19:33:42 No.11215425 Report

Quoted By: >>11215453

I learned graduate linear algebra from Halmos' $finite \ dimensional \ vector \ spaces$ where the build-up of the determinant certainly wasn't as hand-wavy as other anons claim to be rampant in other lin alg textbooks (defenders of Axler). Is it really as "cheap" as other anons are saying? Any examples?

Anonymous

Anonymous Tue 10 Dec 2019 19:34:21 No.11215426 Report

Quoted By:

>>11215253
>I don't care if you dismiss it because it's not in English. I was personally taught linear algebra through this text when I was a first-year first-semester undergraduate. The text properly introduces the determinant in the only mathematically correct way (pic related).
>You live in your bubble with shitty textbooks that give engineer-tier explanations and genuinely think it is sufficient for a pure mathematician? Pretty laughable.
?a??o, ??a??? ?epe? ????oca?? ??e???a?c? :)
????a-?o ca?a ?a?, pe?o??e??ye??? ? ?o???o ?oc?p????a/Ma???a ???a?? ?a?a?, ?o?????e??a? a??e?pa ?a? ? ?o??e, o? ??o? ??oe? ?ep??? pa? c???y. T? c ?e??a?a ca??

Anonymous

Anonymous Tue 10 Dec 2019 19:36:14 No.11215431 Report

Quoted By: >>11217769

>>11214885
> "Linear Algebra Done Right"
It's literally in the title, note the expression "done right", denoting a superiority in methodology........... retard.

Anonymous

Anonymous Tue 10 Dec 2019 19:37:36 No.11215435 Report

Quoted By:

>>11215059
wtf is an exterior form

Anonymous

Anonymous Tue 10 Dec 2019 19:46:53 No.11215453 Report

Quoted By:

>>11215425
Our linalg1 course was pmuch just throwing the det onto our head with no explanations whatsoever

Anonymous

Anonymous Tue 10 Dec 2019 21:57:03 No.11215742 Report

Quoted By:

>>11214242
It's another book by someone who already knows something and thinks they have a "better" way of introducing a subject.
99% of the time your intuition about what's a good way to introduce a subject after you've learned something is wrong.
Not talking about the determinant until the end is retarded, gimmicky, and makes me ill.
Most people who take linear algebra need it to go hand in hand with vector calculus and if you can't even explain what a Jacobian is what's the point.

Anonymous

Anonymous Tue 10 Dec 2019 21:59:33 No.11215749 Report

Quoted By:

>>11214415
No, see that's bass ackward.
It's useless for engineers because engineering needs the determinant and a few other tricks from linalg.
For pure math it's interesting to see a different approach, I guess.

Anonymous

Anonymous Tue 10 Dec 2019 22:48:13 No.11215837 Report

Quoted By: >>11215879 >>11215913

The only nontrivial thing about the determinant is the existence of the signature homomorphism
sgn: S_n - > {-1,1}*. Then you can define a antisymmetric form (,...) such that (e1, ..., e_n)=1, and the fact that it's well defined follows from the existence of sgn. Then define the determinant of A to be (C_1, ..., C_n) where C_i is the i'th column of A. All of the properties of the determinant follows easily from this definition. Literally nothing complicated, nor handwavy. Intuitive too.

Anonymous

Anonymous Tue 10 Dec 2019 23:02:41 No.11215879 Report

Quoted By: >>11215882

>>11215837
>The only nontrivial thing about the determinant is the existence of the signature homomorphism
"No"
It's literally included in the definition of a derivative in R>1.

Anonymous

Anonymous Tue 10 Dec 2019 23:04:11 No.11215882 Report

Quoted By: >>11215911

>>11215879
What do you mean? What's R?

Anonymous

Anonymous Tue 10 Dec 2019 23:09:17 No.11215888 Report

Quoted By:

easy mode

Anonymous

Anonymous Tue 10 Dec 2019 23:17:46 No.11215911 Report

Quoted By:

>>11215882
(you)

Anonymous

Anonymous Tue 10 Dec 2019 23:17:54 No.11215913 Report

Quoted By:

>>11215837
I feel this comes from a mathematicans perspective. Engineer types aren't fans of determinants because they actually must do a bunch of nasty calculations (e.g. compute the determinant of a 5x5 matrix by hand) and then move on to use matlab or never touch upon it again.
A mathematican views it as some homomorphism, writes down the definition, maybe proves some other definition is equivalent to it, but never actually "uses it for something" (by which I mean using it for something that's not math).

>>11214369
That's pretty stupid, imho, at the very latest when you want to succincly define matrix groups like SL.
And at least in dimensions 3 and lower, speaking of volumes, you'd implicitly define the determinant anyhow.

Anonymous

Anonymous Tue 10 Dec 2019 23:39:35 No.11215958 Report

Quoted By:

Who would have thought that avoiding determinants in a Linear Algebra book would generate so much hate kek, it's kinda funny, some people think Axler is the only LA book out there and no one complements their studies with several sources 'heeeeey if you use Axler you'll never learn exterior forms', yeah because I'm only allowed to use one book, right?

Anonymous

Anonymous Wed 11 Dec 2019 00:59:04 No.11216085 Report

Quoted By:

>>11214249
LOL you talking about the A=0 thread aren't you? LOL; If you want to learn linear algebra just don't be lazy and prove all the theorems yourself.

Anonymous

Anonymous Wed 11 Dec 2019 04:05:14 No.11216503 Report

Quoted By:

>>11214543
read the second version then

Anonymous

Anonymous Wed 11 Dec 2019 04:40:42 No.11216582 Report

Quoted By: >>11216674

>>11214242
My reasons for not liking this book:
- the exercises vary from extremely easy to a few absolutely impossible ones spinkled in.
- if you're going to just learn applied LA, there's much better sources like Coding the Matrix/Brown University

There's also the book 'Linear Algebra Done Wrong' which is entirely matrix theory.

Anonymous

Anonymous Wed 11 Dec 2019 05:34:35 No.11216674 Report

Quoted By: >>11216678

>>11216582
>applied LA
It's not applied, but proof-based...

Anonymous

Anonymous Wed 11 Dec 2019 05:38:41 No.11216678 Report

Quoted By: >>11216695

>>11216674
If I only care about applications, I don't really care about proofs. Besides, plenty of application-heavy treatments also include proofs.
If I care about the actual theory, then LADR omits so much that I will still have to read yet another book on LA.

Anonymous

Anonymous Wed 11 Dec 2019 05:53:31 No.11216695 Report

Quoted By: >>11216704 >>11216843

>>11216678
What does it omits, retard?

Anonymous

Anonymous Wed 11 Dec 2019 05:59:20 No.11216704 Report

Quoted By:

>>11216695
Compare the table of contents to Lax or H&K.

Anonymous

Anonymous Wed 11 Dec 2019 07:29:28 No.11216834 Report

Quoted By:

>>11215253
but this is just the usual linear algebra + several/lebesgue analysis anon...

Anonymous

Anonymous Wed 11 Dec 2019 07:38:59 No.11216842 Report

Quoted By:

>Graduate Linear Algebra class
Burgers will always keep surprising me with their laughable education.

Anonymous

Anonymous Wed 11 Dec 2019 07:42:08 No.11216843 Report

Quoted By:

>>11214242
Pseud book for people with no future in brainchad math
>>11216695
imagine posting this

Anonymous

Anonymous Wed 11 Dec 2019 08:08:50 No.11216858 Report

Quoted By: >>11216889 >>11216976

why not introduce determinant early, but axiomatically instead of the horrible formula?

Anonymous

Anonymous Wed 11 Dec 2019 08:31:02 No.11216889 Report

Quoted By: >>11217623

>>11216858
you can actually compute the determinant by reducing a matrix to a triangualr form with gauss-elimination steps and then just multiply all the numbers on the main diagonal together (and also multiply the end result by (-1)^(how many times you did row changes)) so you don't need to remember that formula actually

Anonymous

Anonymous Wed 11 Dec 2019 08:39:52 No.11216896 Report

Quoted By:

>>11215110
I don't think being used as a Grad School course textbook is a plus. What kind of university offers linear algebra as a graduate class, outside of rep theory and the likes?

Anonymous

Anonymous Wed 11 Dec 2019 09:55:04 No.11216976 Report

Quoted By: >>11217620

>>11216858
idk, that is what we do in France.
First, we define the determinant of a family of vectors wrt a basis B as the only alternating form that maps B to 1.
In the process of proving uniqueness, we arrive at the explicit formula.
Then we check that the determinant of a linear map is independent of the basis by general considerations.
Then we define the determinant of a matrix by the explicit formula (having explained why it is a reasonable thing to consider).

Anonymous

Anonymous Wed 11 Dec 2019 17:33:38 No.11217620 Report

Quoted By:

>>11216976
>>11216976
>First, we define the determinant of a family of vectors wrt a basis B as the only alternating form that maps B to 1.
exactly how I would do it.
from the alternating property you can easily derive the geometric meaning - it's how much the family of vectors is scaled in volume compared to the fixed basis (no scalar product needed, it's just ratio). it clearly holds for a set of vectors which are just the basis vectors scaled by constants. then observe what happens when you start making linear combinations (you can mention the Cavalieri principle if you want to be fancy). show that you can always reduce to the easy case and that this process is essentially just gaussian elimination.

Anonymous

Anonymous Wed 11 Dec 2019 17:36:31 No.11217623 Report

Quoted By:

>>11216889
But you can't use gauss-elimination if the entries of the matrix are from a ring like Z rather than a field while the determinant still exists.

Anonymous

Anonymous Wed 11 Dec 2019 18:13:38 No.11217713 Report

Quoted By: >>11217715

>>11214242
People. Why do you think most math books has both instructor's and student's preface? Most books are intended for a university course where there is (at least) a (decent) instructor. When there is a good professor that know about what he is talking. The selft-taugh mathematician is really exceptional case. What we are talking here is proof-based linear algebra (applications are secondary and almost not existent because is not a computational course) where a good professor obviusly wouldn't follow just one book (since when math courses are like reproducing an entire book in the blackboard?). Commonly math courses have big bibliography, although no more than three books are really used.

I was in linear algebra course like this with a very good professor. The course was divided in two parts, the first part used LADR, in an approach not only determinant-free but also coordinate-free where we avoided matrices too and proved all the classic results of vector spaces, euclidean vectors spaces, linear transformations, eigenvalues and polynomials. The last definition was the characteristic polynomial of an operator in terms of the minimal polynomial in slightly different way of Axler's way because my professor also has his own notes in some parts, making some demonstrations easier that the one found in the book, some others coordinate-free, while Axler used matrices (for example, complex spectral theorem). (1/2)

Anonymous

Anonymous Wed 11 Dec 2019 18:14:42 No.11217715 Report

Quoted By:

>>11217713
Then there was the second part of the course, that was all about matrices and we used H&K but most of all was the professor's notes. Only until this moment we saw the gaussian elimination. But before the second part, we defined the isomorphism between vector spaces, between euclidean spaces and between linear algebras. And we showed how, via isomorphism and the (convenient) matrix multiplication definition, all the results we had on transformations and operators also hold on matrices. The final results of the second part was the jordan basis and obviously all that is needed for determinants. Yes, last we proved was the way determinant is used for the basis-independent volume spanned by the n-parallelepiped (with a very convenient use of Gram-Schmidt formula).

The interesting result of this course was that we proved that the determinant-free definition of characteristic polynomial is equivalent to that using determinant (we used jordan basis for this). That is basically the only difference between the classical approach and the "Done Right" approach. I think Axler does the same but in that moment we were just using the notes. (2/2)

Anonymous

Anonymous Wed 11 Dec 2019 18:15:01 No.11217718 Report

Quoted By:

>>11214242
maybe it's actually right

Anonymous

Anonymous Wed 11 Dec 2019 18:42:04 No.11217769 Report

Quoted By:

>>11215431
>t. Tinfoil hat brainlet.
Yeah, let me guess, next you'll tell me the Jews wrote it.

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