Linear Algebra Done Right Book Review

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[@davidk7212]

This book changed my life. It inspired in me a love affair with higher mathematics.

[@BriTheMathGuy]

Glad to hear you enjoyed it so much! Thanks for watching and have a great day.

[@nada3131]

Thank you Brian! Currently taking proof based-linear algebra in undergrad (and using Friedberg and Insel’s a bit more obscure book) this one is a very nice help sometimes 🙂

[@BriTheMathGuy]

Fantastic!

[@malawigw]

The "done right" part of the book also refers to the fact that the author stays away from determinants as long as possible. Often, determinants are introduced quite early in linear algebra courses / books.

[@Mr35diamonds]

Axler hates the determinant approach to linear algebra. I see no problem with it, if it works, it works!

[@hongminh4963]

@@Mr35diamonds I have to agree with Axler about the fact that determinant is not needed for understanding the essence of linear algebra. But at the same time, determinant is a useful tool in many scientific fields.

[@Mr35diamonds]

@@hongminh4963 I used this book for one of my linear algebra courses (it covered the content of the whole book). While I enjoyed the proof based aspects of this book, adequate understanding of determinants are by far one of the most important things in applied linear algebra. IMO the text doesn’t hit quite well in terms of these applications.

[@douglasstrother6584]

The Math Sorcerer would be proud.

[@LazizbekYusupov92]

Hi, Sir. Your comments on this book made my decision straight and my intention strong. I really gonna buy and read it. Thank you!

[@gmcenroe]

This is a remarkable book. The design, content and layout make it extremely readable in my opinion, even for self study.

[@Tehderpduck]

This review makes me feel better, I’m a freshman in college (Applied math) and I loved my first linear algebra class so i got Axler’s book and a few others and I’m able to follow along somewhat well, but somethings are a bit confusing or unclear, so I suppose it makes sense then that it’s meant for graduate study.

[@Nehayadav-zc5gc]

Hello! Can you please help me in proving questions given in this book ?

[@Nehayadav-zc5gc]

I need your help.

[@ashishKjr]

Hello Bri! There's little to no content about Real Analysis on KZbin. Can you review some real analysis book that you liked during your undergrad/grad courses?

[@BriTheMathGuy]

Just made a video for one, here ya go! kzbin.info/www/bejne/Z57bkoqZobynfpY

[@berserker8884]

Pugh's Real Mathematical Analysis is probably the best book on the market, same level as Rudin and takes a much much better approach for a student, like Axler it is very very readable and Pugh acts like your mentor throughout the book. Tho Pugh is for upper division, so if you are just starting out, there is nothing bettwr than Calculus by Michael Spivak. He is basically your personal mentor, as he teaches you to how to do real mathematics throigh the AMAZING problem sets, which you will never find in any other intro analysis book. He will introduce the bare bones to a topic and he will let you develop pretty much everything else through the problems, which will make you feel like you are researching math, but the price is that the problems are ridicolously difficult for someone coming from a highschool math class. Good luck!

[@ashishKjr]

@@berserker8884 thanks for the reply! I have been using Elementary Analysis by Ross and I have been enjoying it so far; self studied from it. I have tried Baby Rudin but its terseness kinda irked me. I'll give it a shot at Pugh for a second reading.

[@hongminh4963]

"This book is intuitive" until I come across the duality of linear map section.

[@spiderjerusalem4009]

why?🤔. The duality map precisely elucidates what matrix tranpose is all about (there is already a vid out there explaining much clearer)

[@Mahmood42978]

Looks a lot like the linear algebra book I used in my graduate class with Dr. Fisher

[@simonegreco4620]

Hey i was searching for a book to buy for autodidact purpose. Nothing too much complicated but complete. Is this completed with exercises? There are others like introduction to Linear algebra by Gilbert Strang and linear algebra by Serge Lang which they say are really good books

[@georgesadler7830]

Thank you for the video. Linear Algebra is used in all levels of Mathematics, Physics, Computer Science and Engineering.

[@josephluna4432]

There aren't the page number 22, only exist the page 7π

[@BriTheMathGuy]

I absolutely love this.

[@ritageraghty4404]

Thank you for review. As a hobbyist, I am relearning maths.

[@BriTheMathGuy]

You’re very welcome. Best of luck with your studies!

[@arthurgames9610]

Is this the book that 3b1b used in his playlist?

[@BriTheMathGuy]

Not sure but that channel is fantastic!

[@adityakhedekar9669]

@@BriTheMathGuy yes it is

[@adityakhedekar9669]

Yes it is

[@TheAcer4666]

So you're reviewing this book but haven't actually read it? Is this just to get clicks on your affiliate link? The only difference between this book and other textbooks is it's got pictures and coloured boxes. The fact it "highlights the important things", "puts examples", and "proof worked out right for you" is what every math textbook does.

[@BriTheMathGuy]

I got through most of it :) . Hope you have a wonderful day!

[@antoniomantovani3147]

it's seems a very easy book, but not superficial and not so abstract

[@jorgeluiscubacalla7534]

Very good , thank you

[@dodgecrockett3474]

I'm a little confused. You said that this is an advanced Linear Algebra text, yet there are no prerequisites for the course. Is this book "part 2" of a series ?

[@benmitchell215]

Is this book ok for a 17 year old ? I’ve been wanting to have a look at linear algebra but I don’t know if I have the skill set yet to approach it. I want to study maths in college and I’ve finished secondary school/high school algebra so would this book be a good next step ?

[@sonicmaths8285]

I've used it when I was 16 y/o so I would say it's quite ok

[@ishaangoud3180]

Have you done Functional Analysis?

[@hopelesssuprem1867]

thanks for the nice review. I like this book

[@josecarlos-zc9hy]

Very thanks, beatiful book

[@BriTheMathGuy]

Have a great day!

[@josecarlos-zc9hy]

@@BriTheMathGuy Equally for you.

[@wachox]

What would be a good follow up book ?

[@enjoyinglife9853]

My class started with row operations

[@cricketfan3507]

Please review linear Algebra Theory intuition code

[@mgupta87]

Thank you for the walkthrough. What's the difference between the third and the second editions?

[@BriTheMathGuy]

You're very welcome. To be perfectly honest I'm not sure of the differences. Have a great day though!

[@alexandertownsend3291]

The third has more exercises.

[@jay22197]

Would you recommend taking this course and probability and stats for engineering at same time for bachelor's?

[@ujwalsmanhas1093]

Hoffman and kunze is still a better book . slightly difficult though.

[@philhwang151]

Thanks! I have considered to buy this book, and I decide to buy now. Have a good day!

[@BriTheMathGuy]

Great to hear. Have a wonderful day!

[@sandilekunene2221]

Can you please do a course videos on it I'm struggling 😭😭😭

[@Ayan4770]

sir pls suggest a book for advanced algebra and group theory

[@plutoniumisotope205]

Aw joshi

[@pinklady7184]

I was looking at this book yesterday at Amazon, but I haven't decided to buy it, at least not yet.

[@Juan-yj2nn]

You should.

[@ericbelmontefuentes4088]

@@Juan-yj2nn is it better and more complete compared with Friedberg’s book?

[@LearnEgTech]

How much price this book ?

[@maalikserebryakov]

Please review strang’s book

[@willnewman9783]

But the book only does things over C and R. I feel like that is a pretty bad thing, as vector spaces over other fields are important for both mathematicians and people who apply math alike

[@vicktorioalhakim3666]

The book does indeed focus on finite dimensional vector spaces, but still I think that it does a great job of keeping the definitions as general and abstract as possible. I haven't seen any linear algebra book that covers theory beyond finite dimensional vector spaces over other fields. Most of that is (and should be) covered by functional analysis books/courses.

[@willnewman9783]

@@vicktorioalhakim3666 I think you misunderstand me. I am not complaining about the focus on finite dimensional vector spaces, I am complaining about the focus on the fields of real numbers and complex numbers. There are many more useful fields that people run across, such as finite fields and number fields, and this book does not talk about vector spaces over a general field, so one may not know what applies to all fields and what applies to just R and C

[@vicktorioalhakim3666]

@@willnewman9783 Take R^n over the rationals. Is that a finite dimensional space?

[@willnewman9783]

@@vicktorioalhakim3666 That has nothing to do with what I am talking about. I am saying that the book does not cover things like Q^n over Q, which is a finite dimensional Q-vector space. It only handles finite dimensional real/complec vector spaces

[@vicktorioalhakim3666]

@@willnewman9783 I think that there is no point of handling finite dim. spaces over fields other than R and C, since these generalize quite easily to any field. The real deal is when you have inf. dim. spaces and those are well treated by functional analysis books. Alternatively, you have plenty of good abstract algebra books, which are more suitable for the spaces you're interested in. Cramming more abstraction in a linear algebra book that is already quite abstract is not useful IMHO, especially when it targets undergrads.

[@wajeehrizvi25]

What are the careers prospects for a math major?

[@BriTheMathGuy]

Going to make a video on this soon!

[@anarchistalhazen7084]

I recommend you read "A Mathematician's survival guide", it discusses everything related to careers

[@asadbabilbabil7791]

Very good

[@vishalacharya5683]

Can anyone suggest linear algebra books with solved examples.

[@BriTheMathGuy]

Depends on which level you're talking about. Schaum's Guide (not sure if I'm spelling that correctly) has tons of fully worked examples. If you're looking for proof based - this book's (Linear Done Right's) solutions are pretty popular online I believe.

[@brookswilliams8020]

Sadly, I think all the answers are online.

[@relytheone853]

Any prerequisites for this book?

[@spiderjerusalem4009]

basic prepositional logic & set theory proof approach. This book is purely algebraic approach, so i would recommend it as second exposure to linAlg, mayhaps in your leisure/holidays/off time whatever since it indeed requires rombust patience

[@ZMhunter]

Does this book uses ̶m̶e̶d̶i̶e̶v̶a̶l̶ imperial system, international system or no units? thanks!

[@BriTheMathGuy]

This book is quite abstract and theoretical, it does not use many units at all. Have a great day!

[@kushpatel6498]

Can you give me this 📚??!,

[@KripkeSaul]

Thanks for the review, but I disagree, although I have not read the book. But a book on linear algebra avoiding determinants and polynomials does not cover much.

[@worththekeeping]

I'd read the book before claiming that

[@laharalal5960]

it does not avoid polynomials, in fact polynomials is the purpose of the book and the determinant-free approach

[@billmorrigan386]

Good video. Yet, I kind of disagree about this book. This is a bit of a misnomer calling a book that way and doing exactly the opposite. It should be called *Linear Algebra Done Wrong: Making Dumbed-Down Incomplete Coverage Look Advanced (just skip on proofs and theory -- people don't get it anyway).* We need another dumbed-down book to cover the rest. Just my opinion. Sorry for the harsh criticism of the book. Now I think that the best first book on Linear Algebra is *Elementary Linear Algebra by Kolman.* The second best (simpler and shorter) is the book by Gilbert Strang. Kolman's text is not very difficult, not too rigorous, not too dumbed-down or non-rigorous. It has derivations, proofs, explanations, applications and all the basics -- around 500-700 pages. Great book. Will work nice with Abstract Algebra by Fraleigh but doesn't require any presupposed knowledge from the reader beyond university calculus. You don't need Abstract Algebra, of course because it's overkill unless you are going to be a mathematician. Well, Kolman is self-sufficient. Not abstract at all but do have all the basics on vector spaces. However for more abstract topics and more depth, I would add Serge Lang's books on Linear Algebra if Kolman is not enough (Kolman is not enough for math majors cause you need a lot of abstract algebra, you need tensors, you need tons of stuff if you want to be a truly pro mathematician). For everybody else, Kolman is perfect, and although it might be a bit challenging it's very healthy for studying hard and for gaining a true understanding without going too far into advanced math. Studying Kolman is very rewarding but it's not a dumbed-down waltz-through. You need to work with the book very seriously. It is similar to Sheldon Ross's book *First Course in Probability (an excellent book for true understanding of Probability Theory) and DiPrima's book on ODE.* These are all topnotch classical books if we have time to really master those areas (usually people just study very, very superficially). Non-mathematicians don't really need abstract algebra but those who want or need it (also rewarding but a different experience!) can study *Abstract Algebra by Fraleigh (one of my favorite books).* It's not difficult as far as books on abstract algebra go. it's only around 600 pages long -- so it's doable if you want to be like 'the sky is my limit' but it's just the tip of the iceberg, just a peek through a spy-hole into modern math, and it can be your first revelation, while *Linear Algebra Done Right by Axler is obfuscation, cutting down on crucial material, putting on airs (of being advanced while being stupid) = a path for rote-learning and snobbery. Once again, sorry for criticism of the book but I doubt people will ever learn anything from it besides memorizing things.* There are almost no explanations, no derivations and huge gaps -- too huge for making even a little bit coherent picture out of linear algebra. The author recommends: You may cover chapter 4 and 9 in fifteen minutes each.... I mean why even bother.... Goes in one ear out the other. It's not even rote-learning. It's a joke. Absence of answers and very few worked problems in sections should also be criticized. But I don't criticize his approach eschewing determinants, nor do I criticize 'verify yourself' or 'fill in the skipped steps' in the proofs given by the author -- it's not a bad practice, and if done right it is a good thought-provoking tool reducing rote-learning, but I'm afraid it was botched up too in this book. Well, it could have been a good book but it is not. In my opinion it's a disaster for a future mathematician. For non-mathematicians and rote-learners it should be fine. Such short books are no go when they try to cover too much. The irony is that it supposedly targets future mathematicians but they will be fine anyway 'cause they have dozens if not hundreds of math books anyway. I'd give this book no more than 2 stars out of 5.

[@billmorrigan386]

@hobo doc You're welcome. I just took one more look at this Algebra Done Right after watching your review. And just can't reconcile myself with superficialness of the book. It could have been a good book if the concepts were a bit more developed. But your reviews and recommendations are very good. This book is not that bad, and it could be an addition to main books on linear algebra, I guess. It is kinda too terse, I guess. Probably not bad for browsing through at leisure. But it casts doubts on the qualification of the author. Serious doubts. I mean dismissing or dispensing math like that is kinda -- I don't know even how to put it.

[@billmorrigan386]

​@hobo doc ​ Yeah, exactly. Diverse sources are necessary for more complete, finished picture. And sometimes a shorter, simpler book is a good start before plowing through something too large with excessive details. The higher we go, the more difficult the details and derivations become, that is, the more abstract, more advanced, and more generalized they become. I have come to the conclusion that textbooks should be of right size and rigor. Too much terseness and superficiality are detrimental to proper understanding and contemplating things. So, I always feel like I need at least one book that is really big and rigorous so that I can verify and go into a lot of detail concerning any aspect I deem necessary to delve very deep in. As of now I know no such book in linear algebra but a number of disparate books tackling separate aspects of linear algebra very deep. It still gives the full picture of course but I like seeing and studying books like Courant's Calculus, Thomas's Calculus, Kolman's linear algebra (for beginners), Sheldon Ross's First Course in Probability, Spivak's Calculus (one variable only) and Vector and Tensor Analysis by Brand, Analytic Geometry by Douglas, Abstract Algebra by Fraleigh, GDE by DiPrima etc. Although something shorter or simpler might look like a better idea, e.g. Apostol's Calculus, in reality it would be just bits and pieces of information and we would not see the forest for the trees with such books. Yet everybody praises them. Math will never reveal itself through such books. But they are good books all right. I especially liked your video because you don't advise Apostol's books. Advising it is tantamount to saying if you want a good watch, then go buy a Rolex. It's a good brand and somewhat good advice but at the same time such advice is also stupid and useless, if not even detrimental. I ain't kidding. Giving a kid Apostol's Calculus may kill all the interest in math. That said, Apostol is a good book all right. The best thing is diversity. Could not agree more with that. *Still sometimes I want to see a 'proper' book, i.e. not the one which is just a proverbial show-off that keeps the true picture, the true nature, and the true spirit and beauty of math behind a veil, behind a very long disparate list of theorems rigorously and elegantly proofed in modern notation.*

[@billmorrigan386]

​@@cktan8439 For an SAT math (algebra II exam), no dedicated linear algebra book is needed. You only need basics which are covered in superb books like Algebra and Trigonometry by Stewart (or the same title by Larson, or by Swokowski). Such books (more than 1000 pages) cover HS math thoroughly. Once all the math in such a book has been studied (you might want to focus on the parts featured on an SAT exam, not on everything in such a book), just practice with prep books (for math SAT) by such publishers as Barrons, Princeton, etc. I mean once you learned math well, you just need to practice and do as many mock exams as possible striving for the best scores possible. The HS curriculum and SAT math cover only the basics when it comes to linear algebra. It's just matrices and determinants. There's not much more than that on an SAT exam in terms of linear algebra. It can be learned in a day. Well, not really. I'm a little exaggerating. However, the math GRE (for math majors who want to go on studying math to get a master's degree) will require more linear algebra and a dedicated book on it. So, a very serious college student who wants to know linear algebra really deep and well might try the Elementary Linear Algebra by Kolman. If that's too much, the book by Gilbert Strang is also top notch. But none of it is needed for the SAT. That's because the SAT math has no linear algebra, except for rudimentary operations with matrices and determinants. My best piece of advice is to get a comprehensive book titled Algebra and Trigonometry (as I said in the beginning); it won't go amiss because you will need some elementary HS math in college. You might also want not the latest edition as the latter might be pricey and bloated, and I see no difference with previous editions anyway. In college, most students struggle with calculus and other math subjects. That's because they have never held a proper book on algebra and trigonometry in their hands, and because our HS math curriculum is nothing but a joke. Truth hurts. The books I recommended have almost 100 pages dedicated to matrices and determinants. That should suffice for acing an SAT math test.

[@billmorrigan386]

​@@cktan8439 If you struggle with basic algebra, this is my advice: Algebra and Trigonometry by Larson or the same title by Stewart (for acing SAT math) + First Course in Calculus by Lang (for acing AP Calculus). That's it. Well, for acing them, you, of course, need to solve a lot of mock tests! You can prepare with mock tests through publishers like Barron's, Princeton, McGraw Hill, etc. They have good books for acing AP Calculus and Math SAT with lots of mock tests. But before practicing mock tests you already need to know the subject very well. Kline's text is superb but it's not a good idea if you struggle with HS algebra or cannot already ace a math SAT. First course in Calculus by Serge Lang is for beginners, i.e. for ambitious HS students. It will help you to ace AP Calculus or it will make things easier when in college. Many students struggle with calculus in college, although they did well in math when in high school. If you do very well, you may then take up Calculus by Larson (or by Stewart or by Kline). Kline's text is a little different however. It would be good to combine it with Larson's in my opinion. But right now, I would concentrate on Algebra and Trigonometry by Larson (or by Stewart, or by Swokowski). SAT math tests have no rigor and no math abstractions. They are very basic speed tests, i.e. if you know math well, you will be able to solve primitive problems faster than others. So, SAT math checks if you are proficient enough to solve everything very fast. That's all. It's very basic primitive elementary math only. That's what the SAT math is all about. It's even laughable if you should ask me. Yet, the speed shows who is who.

[@nojuri1143]

​@@billmorrigan386 ​ Thanks for your review! I'm quite enjoying the book right now: I go through proofs slowly and understand them logically, though I agree that it's a bit too terse at times, and more concrete examples (preferably visually) would be appealing. For instance, I don't have an intuition how dual spaces and annihilators relate (how can I understand visually that the range of a linear map is the same as the annihilator of null space of this map). Also, intuitive grasp of Polar Decomposition, and how its parts (the isometry and the square root of T and its adjoint) make up for the original map. For that, I feel like another book, more concrete and visual, would supplement my self-study very well. I've checked some of the books you've referenced (by Kolman, Strang (great lecture series he has!), and Lang), but they didn't seem to cover these topics (especially on duality). Do you have any recommendations? Thanks!