I need to learn linear algebra over the summer, I've heard good things about this textbook and I saw it has a new edition that came out this year. Has anyone read it? What's your favorite linear algebra textbook?

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# linear algebra textbooks

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I need to learn linear algebra over the summer, I've heard good things about this textbook and I saw it has a new edition that came out this year. Has anyone read it? What's your favorite linear algebra textbook?

It's OK but the author insists on not using determinants so has to do eigenvalues in a very unorthodox way. Try Friedberg/Insel/Spence instead.

That one you recommended is so expensive...

Has anyone read this one? It's basically free. Or what about The Manga Guide to Linear Algebra?

that book isn't rigorous at all which is fine if you only care about computational linear algebra

>Manga Guide to Linear Algebra

is axler and this meme book all you could find in the archives lol

Hefferon is a meme. Garbage written for CS grads written by a brainlet who doesn't understand linear algebra to begin with. You're better off reading random lecture notes than that abortion

Read the manga guide

>OP asks for book recs

>immediately disappears, leaving his thread to die

bot thread

It's definitely better early on, not just dumping out the definition of the determinant like some magical formula from on high, but it does really tie itself in knots later on.

the best way to introduce the determinant IMO is to introduce it as the general solutions for linear systems . Then you show the geometrical meaning and then proceed with your abstract bullshit so that you can call yourself a mathematician and not an engineer

Gorodentsev. Algebra

It basically introduces algebra using linear algebra and in turn treats linear algebra much more in-depth than the usual lin alg book

seconding these. They've some of the best exercises I've ever come across in a textbook. Sternberg's way of doing calculus on manifolds is also extraordinarily based

I swear this board has the stupidest autists when it comes to book recommendations. Do you really think it is feasible to learn linear algebra from self study over a SUMMER from this book?

read 10 pages a day and you'll be done in two months. No need to do all the problems, the exercises have solutions

>read 10 pages a day and you'll be done in two months.

You can say this with any book, idiot. Better to pick a book focues on Linear Algebra if that is what you want/need to learn.

>No need to do all the problems,

Of course you won't do EVERY single problem in a book, but doing problems is very important and more time should be done doing that than reading.

>its absolutely doable if youre not a brainlet.

Shut up idiot, I know you didn't learn Linear Algebra or even any math subject over the summer from a book.

>His proofs are also very concise

Yeah, because that is perfect for self-study in a limited timeframe. Moron.

So you know frick all about the book but are hell-bent on hating it. I will now hide your shitposts

I'm not "hating" on the book you idiot.

>>His proofs are also very concise

>Yeah, because that is perfect for self-study in a limited timeframe

i know youre not very smart but trimming the fat is actually great for self study. Proofs shouldnt be novels. Actually try passing any math exam when you're incapable of concisely expressing yourself kek

>I know you didn't learn Linear Algebra or even any math subject over the summer

why project lol. Ive read several books over the summer and even during university. i havent completed gorodentsev but read enough to know it's one of the more pedagogically valiable algebra books

as for the other nonsense you said

>doing problems is very important and more time should be done doing that than reading.

you should spend most of your time comprehending the theory and proofs to then use those or similar techniques and ideas in your own proofs. problem solving can be a waste of time if you massively lack the resources for a problem, just look at all the schizos here trying to prove millennium prize problems.

>Actually try passing any math exam when you're incapable of concisely expressing yourself kek

Deciphering a concise proof and writing a concise proof are two different things, genius.

>Ive read several books over the summer and even during university.

Doesn't mean anything. I asked if you LEARNED a subject over the summer from a book. You haven't. If you don't care how much you absorb or how far you get, then reading any book is fine.

>you should spend most of your time comprehending the theory

How can you "comprehend" the theory without doing problems?

>and proofs?

Making sure you understand and can follow proofs is good, but you should also be able to write your own proofs. Also, computational problems help with understanding. And if you can't solve a 4x4 system by hand on paper (given enough time) then you suck at linear algebra.

>problem solving can be a waste of time if you massively lack the resources for a problem, just look at all the schizos here trying to prove millennium prize problems.

What the frick are you talking about? OP wants to learn basic linear algebra. I bet they are barely out of the calculus sequence.

>Deciphering a concise proof and writing a concise proof are two different things

You learn to write concise proofs by reading them in the first place. Break them down to know what's necessary to include and what's not. Overly wordy proofs tend to be more confusing than helpful. Any grad student knows this. You even have books like Kallenberg's probability explicitly mentioning that in the preface.

>How can you "comprehend" the theory without doing problems?

By working out the ideas that make the proof work and coming up with your own examples (get into research and you'll see that it is possible to learn about something without doing exercises). Not to mention, Gorodentsev differentiates between exercises and problems.

>computational problems help with understanding

You can easily come up with these yourself but Goro includes a few nontrivial ones too. In any case, it can be largely useless too, like inverting a large matrix over the field of 4 elements.

>What the frick are you talking about?

It's clear once you read more math books. You shouldn't waste too much time on unreasonable problems. Some authors also like to put open problems in their books.

>Doesn't mean anything. I asked if you LEARNED a subject over the summer from a book

I have. I memorized the proof ideas and techniques and successfully applied them in my research and coursework. I've also solved quite many exercises in a lot of them and come up with my own examples and applications.

You can learn a lot from books and certainly finish a 400+ page one within a few months if you're motivated. Even the reading courses at my university tackle bigger books over the summer.

Just stop assuming OP is some apathetic moron

>Just stop assuming OP is some apathetic moron

Dude, you're suggesting OP learn linear algebra from a graduate book that includes a lot of unnecessary material. You're an idiot.

>i know youre not very smart but trimming the fat is actually great for self study.

I find it funny that you claim I'm not smart when you type like a sixth grader.

Kek

it's nice, right

based

its absolutely doable if youre not a brainlet. Ive read some chapters of gorodentsev before and hes very good at motivating whatever he'll introduce and incorporating all the advanced algebra meaningfully, puiseux series were done particularly well. His proofs are also very concise

>Gorodentsev. Algebra

https://www.youtube.com/playlist?list=PLq3E5oubNNoBDXd2qvs2WF17L6az7MzCM

Lectures by the author

/mg/ approves

Shlomo Sternberg's Advanced Calculus. Does both analysis and linear algebra

based

The book is too difficult and at the same time shallow. One of the worst book ever written. Not appropriate for anymore.

It's not like doing multivariable calculus with differential forms and manifolds is such an obscure topic today.

It's a meme answer. Ignore it OP.

I honestly think it's more efficient to go through a problem book. Like Halmos' or John Erdman's.

Sternberg's treatment of ODEs and classical mechanics is very based though. I agree that some exercises are ball-bustingly difficult though

If you need to use Axler, use it as a supplement to Harvard's Math55 or else you'll miss out on a lot of important math

>another "how do i learn x" thread

*yawn* just follow the /mg/ curriculum https://sheafification.com/the-fast-track/

Just use Shilov. It's concise and cheap.

Katznelson's Terse Introduction into Linear Algebra. Short and great exercises

Actually good recommendation

"Advanced Linear Algebra" provided you're not a brainlet

Roman's book is actually good and not all that advanced. I'm pretty sure most undergrads could read it just fine

Blyth's module theory

Dieudonné

Greub

just start reading lazy gay.

Bourbaki Algebre 1-3

Lang's algebra has a great chapter in linear algebraä

Op, just pick whatever book your university uses for the intro linear algebra course or look up what is commonly used in intro courses. Do problems and supplement with online notes and ask questions online.

Seconding this OP, every linear algebra book is missing /something/ (in Axler’s case, determinants) so you’ll do best with a syllabus or course notes to guide you.

Lin alg. is easy, you just need to grind problem sets

I have to take calc 1 this summer, any advice? I’m not Asian or white btw.

Start here

Calculus With Applications Peter Lax

Amann Escher, Analysis I.

Sternberg, Advanced Calculus

Finite-Dimensional Vector Spaces Halmos

If you're an Engineering student, read pic rel and save yourself from all the rigor bullshit.

It also has sections when it goes through the real life application of concepts in linear algebra

literally useless

You are useless

Can concur.

Can Concur

what about this? it’s linear algebra applied to calculus.

anything similar but for differential equations?

if someone recommends Axler's book he is full of shit and never read it. completely useless book

>>no mention of hoffman and kunze

IQfy has fallen

While I can't provide personal opinions or experiences, I can offer some insights into popular linear algebra textbooks based on reviews and recommendations.

One highly regarded linear algebra textbook is "Linear Algebra and Its Applications" by David C. Lay, Steven R. Lay, and Judi J. McDonald. It's known for its clear explanations, numerous examples, and practical applications of linear algebra concepts. Many students and instructors find it accessible and comprehensive for learning linear algebra.

Another popular choice is "Introduction to Linear Algebra" by Gilbert Strang. This textbook is praised for its intuitive explanations and emphasis on geometric interpretations of linear algebra concepts. It's often recommended for its readability and clarity, especially for those new to the subject.

Additionally, "Linear Algebra Done Right" by Sheldon Axler is well-regarded for its rigorous approach to linear algebra. It focuses on conceptual understanding and proofs, making it suitable for students interested in a deeper understanding of the subject.

Ultimately, the best linear algebra textbook for you will depend on your learning style, mathematical background, and personal preferences. It may be helpful to browse through the table of contents, read reviews, and perhaps even sample a few chapters to see which book resonates with you the most.

Thanks chatgpt.

https://www.youtube.com/@TheMathSorcerer

Gorodentsev for undergrad and Lang for grad is the /mg/ curriculum

>Basic Set Theory and Algebra: Hints on Representation, Topology, Geometry, Analysis

https://arxiv.org/pdf/2101.02031.pdf

Category theory propaganda

>book about category theory

>finished in 2021

Poor guy. If he’d done this 10 years sooner, he would have been employable

what about Linear Algebra by Shilov?

axler is alright, don't know why people are hating on this book

>axler is alright, don't know why people are hating on this book

Because determinants are haram for him so he "defines" the characteristic polynomial first as (z-λ1)...(z-λn) only for the complex case then has to explain complexification and tie himself into knot for the real case and who cares for arbitrary fields lol while sane people just go with det(A- λI) and call it a day.

If you want a braindead/CS-tier overall outlook on Linear Algebra (or glorified exercise book)

>Anton

>Lay

>Strang

If you want somewhat rigorous book

>Kunze

>Insel/Spence/Friedberg

>Pelletier

If you want to go ham, and don't mind slavrunes.

>A.Г. Кypoш - Кypc Bыcшeй Aлгeбpы

>Ильин, Пoзняк - Линeйнaя Aлгeбpa

>Бeклeмишeв - Кypc Aнaлитичecкoй Гeoмeтpии и Линeйнoй Aлгeбpы

>If you want a braindead/CS-tier overall outlook on Linear Algebra (or glorified exercise book)

>>Lay

>If you want somewhat rigorous book

I took a lower division class with Anton, then an upper division class with Insel/Spence/Friedberg. I felt well-prepared. Granted, I had a really good teacher for the first course. Maybe some are fine skipping books like this, but I don't recommend it.