Best Resources for Learning Linear Algebra

ORIGINAL POST

Basically how can I pick up the basics of Linear Algebra on my own. I don't need to become an expert in the subject, I just want to learn enough that I can apply it to computer science and maybe continue to build on my knowledge in the future.

At this point I know very little about the subject: I know the basics of vector arithmetic, scalar multiplication, etc. so I'm more or less starting from scratch.

5 replies

supposenot · 5 years ago

Lay's Linear Algebra and its Applications is a pretty good text (I used it for my first two courses) and there's a free pdf download online.

If you want alternate presentations of things in that book, I would check out the 18.06 lecture series on MIT OCW. You can get a full playlist here: youtube.com/watch?v=7UJ4CFRGd-U&list=PL221E2BBF13BECF6C.

2 upvotes on reddit

wrangsdad · 5 years ago

This series is pretty great, won’t be everything you need but it’s a great reference and is really helpful to understand what linear algebra actually is. Essence of Linear Algebra

1 upvotes on reddit

lead999x · OP · 5 years ago

I watched some of that one already and 3B1B is always awesome! I don't mean to sound unappreciative but I think I need something less high level.

1 upvotes on reddit

wrangsdad · 5 years ago

Lol no worries! I’m in linear algebra right now and am doing well and take all my notes on my iPad and have classmates that are struggling so I’m going to be making a google drive folder to share with them, I wouldn’t mind sharing with you as well if you’re interested!

2 upvotes on reddit

wrangsdad · 5 years ago

Also btw I’m studying comp sci too!

2 upvotes on reddit

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r/mathematics • [2]

Summarize

Linear Algebra: resources?

Posted by ZookeepergameSoft301 · in r/mathematics · 3 months ago

Hey everyone! I hoping to learn linear algebra from scratch to advanced also with its applications in industry using matlab or wolfram. Any resources which would help me with this ? Ps : I’ve started gilbert strang’s lectures on yt

6 upvotes on reddit

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SimonBrandner · 3 months ago

The 3Blue1Brown linear algebra series is excellent for building up a geometrical intuition for things

1 upvotes on reddit

fresnarus · 3 months ago

If you want a much more advanced book than Strang, get a hold of Halmos's "Finite dimensional vector spaces", but make sure you know what a mathematical proof is, and how to come up with them yourselves.

There are much more advanced treatments of linear algebra than Halmos (for example Bhatia's "Matrix Analysis" book). However, that is deep stuff, and not for beginners.

1 upvotes on reddit

SnooCakes3068 · 3 months ago

Also read strang’s textbook. Best yet also read linear algebra done right by alxer.

2 upvotes on reddit

Hoid_99 · 3 months ago

Elementary Linear Algebra by Howard Anton is really good

2 upvotes on reddit

srsNDavis · 3 months ago

Besides the OCW lectures, Strang has a book too, I highly recommend getting familiar with reading maths.

3Blue1Brown's videos are phenomenal for building your intuition around linear algebra.

MATLAB/Wolfram: I'd look on YouTube. Or the official courses (example).

1 upvotes on reddit

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r/learnmath • [3]

Summarize

Resources for learning linear algebra?

Posted by rickyrichboy · in r/learnmath · 7 years ago

Does anyone know of any good online resources for learning linear algebra (web series, practice problems, etc)? I’m taking it right now in college and the professor isn’t very good, so I’m hoping to find some resources that will help me understand what we’re learning in class!

1 upvotes on reddit

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r/https://youtu.be/fNk_zzaMoSs

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playingsolo314 · 7 years ago

Linear algebra is a vast subject. Are you just doing matrices and solving linear systems? Or vector spaces? Tensor products? We can help better if you provide more detail

1 upvotes on reddit

akai_hige · 7 years ago

I've always enjoyed 3Blue1Brown's YouTube content. He is very good at creating visual arguments for what is being explained.

2 upvotes on reddit

o_edo · 6 years ago

Here a nice course for beginners. For free. Nicely illustrated. http://studybyyourself.com/seminar/linear-algebra/course/?lang=en.

1 upvotes on reddit

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r/mathematics • [4]

Summarize

What are some good free online resources to learn linear algebra?

Posted by TravellingBeard · in r/mathematics · 3 years ago

I've always been interested in machine learning but understanding it beyond the most basic 3 layer neural net will require linear algebra. I took it in university as part of my computer science degree but it was a struggle, so hopefully things have gotten much better, especially with videos and illustrations.

There is the default, Khan Academy, normally a great choice, but wondering if you know of any other good resources?

3 upvotes on reddit

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https://www.youtube.com/watch?v=WJfolPLC5tg&list=PLfbradAXv9x7nZBnh_eqCqVwJzjFgTXu_&ab_channel=Math%2CPhysics%2CEngineering

7 replies

MathPhysicsEngineer · 3 years ago

If you have prior knowladge and you wish to refresh and strenthen it I would sugest this playlist:

it also comes with lecturenotes:

https://drive.google.com/file/d/1HSUT7UMSzIWuyfncSYKuadoQm9pDlZ_3/view

1 upvotes on reddit

mangotopia · 3 years ago

In addition to those already mentioned Kimberly Brehm’s got a lecture series that I’m finding very useful.

https://youtube.com/playlist?list=PLl-gb0E4MII03hiCrZa7YqxUMEeEPmZqK

4 upvotes on reddit

TravellingBeard · OP · 3 years ago

Thank you very much!

1 upvotes on reddit

tenebris18 · 3 years ago

There's an MIT OCW course by Gilbert Strang which I liked. The plus is that he also has a book on the subject which you can refer to.

3 upvotes on reddit

TravellingBeard · OP · 3 years ago

Thanks!

1 upvotes on reddit

GauravChandan · 3 years ago

The YouTube channel 3blue1brown by Grant Sanderson has a series of videos called 'Essence of Linear Algebra' which is quite popular. Definitely worth checking out.

3 upvotes on reddit

TravellingBeard · OP · 3 years ago

Thank you!

1 upvotes on reddit

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r/learnmachinelearning • [5]

Summarize

what are the best Linear algebra resources? and how to learn math?

Posted by i3zM · in r/learnmachinelearning · 4 years ago

hello, last year I've learned some ML algorithms, and I've made around 5 projects.

and i just graduated from high school so I want to learn more about the

mathematics of Machine Learning before getting into university,

and I'll start in linear algebra, any recommendations or tips?

Mathematics for Machine Learning Course (Coursera)

this Course is good, I took half of the Linear algebra course,

but I want to grasp deeper knowledge

Mathematics for Machine Learning Book

this book is great, but I want to learn more and build a good foundation in these topics.

so most likely I won't go with it.

i have 2 choices for now

1:Linear algebra by Prof. Gilbert Strang

a lot of people recommended this course but I feel that it's too old.

2:Linear algebra Done Right

this book is great and here's a full explanation of the book from the author.

i guess these are my choices and if you have any

tips or recommendations for Linear algebra, Calculus, and Probability & Statistics,

please write them down.

and what's your approach guys in learning math,

because I feel that it's too hard to use the spaced repetition technique in Mathematics.

I mean the learning process gonna be long, so I have to figure out the best way to learn

so I can grasp the Concepts and the topics well.

;)

4 upvotes on reddit

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axetobe_ML · 4 years ago

I have not used these frameworks yet. But these look promising.

How to Teach Yourself Math by Scott Young A framework on how to find insights when learning maths.

Learn Difficult Concepts with the ADEPT Method A strategy used to help get an intuitive understanding of a maths topic.

1 upvotes on reddit

save_the_panda_bears · 4 years ago

Why do you feel Gilbert Strang's course is too old? The fundamental principles of linear algebra haven't exactly changed in about 100 years.

3 upvotes on reddit

Wonderful_Goat_4011 · 3 years ago

I do not know why I am not able to understand from him.

1 upvotes on reddit

i3zM · OP · 4 years ago

oh sorry, i didn't make it clear.

i mean the recording is too old.

1 upvotes on reddit

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r/learnmath • [6]

Summarize

Online resources for Linear Algebra

Posted by [deleted] · in r/learnmath · 4 years ago

I need some extra help trying to learn the concepts of linear algebra. I know of Khan Academy and 3Blue1Brown on youtube but I was wondering if anyone can suggest other websites or youtube channels to check out.

10 upvotes on reddit

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https://youtube.com/playlist?list=PLscpLh9rN1Rfo0ifw9RZFoJ2Te2jk_pwX

5 replies

CoffeeAndCalcWithDrW · 4 years ago

I taught Linear last year. These are the videos I made for my students. They are all extra practice problems and solutions.

2 upvotes on reddit

vikingville · 4 years ago

https://www.edx.org/course/linear-algebra-foundations-to-frontiers

3 upvotes on reddit

[deleted] · 4 years ago

https://hefferon.net/linearalgebra/index.html

chapters, exercises and solutions.

3 upvotes on reddit

belon94 · 4 years ago

Try this one

https://cloud.sowiso.nl/courses/chapters/en/6

3 upvotes on reddit

Machvel · 4 years ago

if you have not seen it, strangs linear algebra lectures on youtube are great, his textbook is not as great in my opinion though. his website has a ton of old linear algebra exams, which are really good for practice.

5 upvotes on reddit

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r/OMSCS • [7]

Summarize

Linear algebra - best resources?

Posted by whyareell · in r/OMSCS · 2 years ago

Hey everyone, I am starting in Fall 2023. I am hoping to brush up on my linear algebra which I last studied some 20 years ago. I am not in a rush since I don’t need linear algebra for the first few courses I have planned. But rather I want to build a strong intuitive understanding, which is how I do math best. I tried doing the GT edX course, but I feel like it mostly deals with the mechanics of how to calculate stuff rather than intuitively understanding what it means. Some options that have been previously suggested on this sub Reddit are listed below - if any of you took these, could you comment on how you liked it?

Khan academy linear algebra
UT Austin Linear Algebra - Foundations to Frontiers (LAFF)
MIT OCW Linear Algebra
Any other courses recommendations?
Any textbook recommendations?

23 upvotes on reddit

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https://drive.google.com/drive/folders/1J7ndpMeg8Dx_XcV_Vg5ddGStHIi5neeM

12 replies

lucy_19 · 2 years ago

Mit ocw. Gilbert Strang is very very good for linear algebra. Plus you have all the hws, exams and even problems specific to lessons to practice.

5 upvotes on reddit

diesmilingxx · 2 years ago

is the videos from 14 years ago still good? or are there specific playlist? https://youtube.com/playlist?list=PL49CF3715CB9EF31D

1 upvotes on reddit

lucy_19 · 2 years ago

Yes. I’d suggest going to mit ocw website and finding the sc section of the course. You’ll find everything neatly organised there. Each lesson also mentions the related readings from the book, so if you don’t understand something you can always read the relevant sections from the book. This is tailored to the latest edition of the book if I’m not wrong, so you don’t have to worry about missing out on anything.

2 upvotes on reddit

Tvicker · 2 years ago

of course they are good, linear algebra is not something which is fast moving

2 upvotes on reddit

hedoeswhathewants · 2 years ago

3blue1brown has a good series on the intuition behind linear algebra.

11 upvotes on reddit

Wild-Thymes · 2 years ago

I was going to recommend this. 3blue1brown does not provide the mechanical steps, but he helps you build the intuition to internalize the concepts very well

3 upvotes on reddit

whyareell · OP · 2 years ago

That’s the YouTube channel right? Ah thank you! I had stumbled on a really good video some time back, but couldn’t find it again. I think it was this one!!!

3 upvotes on reddit

Aggressive_Aspect399 · 2 years ago

The Schaum’s book on Linear Algebra is relatively cheap, well written, and has many examples.

1 upvotes on reddit

[deleted] · 2 years ago

Notes from when I was a linear algebra instructor in a past life:

5 upvotes on reddit

[deleted] · 2 years ago

I don't necessarily recommend them over the other resources you've mentioned, but I'm happy to share them.

1 upvotes on reddit

whyareell · OP · 2 years ago

Thanks all, I will get started with his lectures on MIT OCW (unless there is a different set of lectures?)

4 upvotes on reddit

whyareell · OP · 2 years ago

I believe he is the one teaching the MIT OCW course?

2 upvotes on reddit

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r/askmath • [8]

Summarize

Looking for a great Linear Algebra book (learning after a long break)

Posted by AMMAR-TAHIR · in r/askmath · 3 months ago

Hi everyone,

I’m looking to dive back into Linear Algebra, but I’m having a hard time finding the right book. I studied university-level math about 20 years ago, so while the foundation is there somewhere in the back of my mind, I definitely need a refresh, ideally something that’s rigorous but also explains the intuition clearly.

I’m not looking for a quick reference or just exercises, but a book that helps me understand and rebuild my thinking. I’d really appreciate recommendations that worked well for others in a similar situation.

Thanks a lot in advance! 😊

6 upvotes on reddit

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Weird_Rush_3328 · 3 months ago

Your welcome. He has free videos on YouTube. A complete course in linear algebra from mit

1 upvotes on reddit

CraftySeer · 3 months ago

Linear Algebra for Data Science by Cohen on OReilly press is working for me. Comes with a GitHub repo as it teaches both theory and code in python.

2 upvotes on reddit

AMMAR-TAHIR · OP · 3 months ago

I have heard of this one, did not lnow about the github though, thanks!!

1 upvotes on reddit

Glum_Revolution_953 · 3 months ago

i used otto bretscher linear algebra for my class. had to take linear algebra after my bachelors to get into stat grad programs since i wasn't a math major

2 upvotes on reddit

AMMAR-TAHIR · OP · 3 months ago

Thanks

2 upvotes on reddit

Vivid-End-9792 · 3 months ago

I was in a similar spot, and “Linear Algebra Done Right” by Sheldon Axler really helped, it’s rigorous but explains why things work, not just how. If you’d like more intuition and geometry, Gilbert Strang’s “Introduction to Linear Algebra” is fantastic too. Both do a great job reconnecting the theory to the bigger picture rather than feeling like a list of techniques.

2 upvotes on reddit

AMMAR-TAHIR · OP · 3 months ago

Thank you for your input!

2 upvotes on reddit

Character_Range_4931 · 3 months ago

Linear Algebra done right by Sheldon Axler is probably the best one. The treatment of most linear algebra texts is that from the perspective of matrices and operations on them, especially with the use of the determinant. In my opinion (and evidently the author’s opinion as well) this is a very unenlightening, algebraic way to look the subject. But if you approach the subject from the perspective of linear maps first, a lot of the subject matter becomes easier to understand (at the cost of more involved proofs). For example, the typical proof that there is always an eigenvalue for any linear map in any odd-dimensional vector space follows by considering the determinant of the matrix A-λI while Sheldon Axler approaches it by considering the minimum polynomial (the unique monic polynomial of smallest degree that annihilates the operator). I also liked that it introduces matrices as a consequence of linear maps, while most texts do it the other way around. This helps in my opinion with many questions like “why can’t we divide matrices” by making the analogy of “why can’t we divide by functions?”: because it makes no sense. When I say f(x)=y, do you think to divide by f? I guess it depends on what you want linear algebra for. If you want a theoretical knowledge of the subject, definitely go for this book. Otherwise, if you want a computational perspective, I’m sure any book works, Lay/Strang/Larson are the typical recommendations I believe.

2 upvotes on reddit

Uli_Minati · 3 months ago

You can "divide by" a matrix by multiplying with its (multiplicative) inverse, same as division of real numbers

You can "divide by" a function if you first define what it means to "multiply" a function

0 upvotes on reddit

Character_Range_4931 · 3 months ago

You can’t divide by a matrix. You’re just applying the inverse map. The analogy was meant to liken multiplying by the inverse to taking an inverse function. How do we solve f(x)=y? You take the inverse and get x=f^-1(y). (Given that the inverse exists). Now a linear map T on a vector space with a given basis is isomorphic to a matrix M(T). If the map is invertible, T^-1 is also a linear map such that T^-1 T=I (much like function composition). So since the inverse is also a linear map, it too is isomorphic to a matrix M(T^-1) (we take the matrix wrt the same basis as that of T). Then M(T)M(T^-1)=M(TT^-1)=M(I) is the identity matrix. This is how we “divide” by matrices. But we never divided by the matrix. We just used properties of linear maps and the isomorphism M from linear maps to matrices. The thing is people treat matrices as “just an generalisation of R” and that we can do everything with matrices as we can in R, but they’re kind of different things.

1 upvotes on reddit

Numbersuu · 3 months ago

Clearly f(x)=y gives (x)=y/f after dividing by f

1 upvotes on reddit

AMMAR-TAHIR · OP · 3 months ago

Thanks for your detailed feedback!

1 upvotes on reddit

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r/learnmath • [9]

Summarize

Best Linear Algebra material I've found so far

Posted by need_friends137 · in r/learnmath · 3 years ago

This is my own response to a question I've posted here: Original purpose

What I was trying to ask in that post was simply some online material to learn L.A as a mathematician (at least close). Keeping it short, most materials on internet, which sometimes are reflection of our school system, are kind of Wikipedia-ish. I've tried all kind of standard materials like Gilbert Strang's, David Poole, Sheldon Axler and Sergei Treil, but I wasn't getting it quite right.

So, I wanted something like this: Essence of Linear Algebra, by 3blue1Brown, which really showed the beauty of L.A; but I wanted something more complete. And I've found this amazing course: Essence of Linear Algebra, by MathTheBeautiful, which keeps the qualities of 3B1B, showing the power of creativity, deduction, pattern recognition and etc etc. Both materials are very different from the standard School/College approach. I'm watching this for 2-3 months now, but I thought I should post this for people in same position as I was.

P.S: I'm not them, nor I know them, nor I was paid.

67 upvotes on reddit

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Machvel · 3 years ago

why was axler not a good fit for you? i found it to be the best linear algebra resource i have come across anywhere

7 upvotes on reddit

need_friends137 · OP · 3 years ago

Sincerely, I'm not good at expressing myself to people. Most of the time people get me wrong. I'm not that good at social "things". Maybe someone else in future will see this post, and know what I'm trying to say. But maybe these materials (the standard ones) are better for people more interested into applications or how it works instead of why it works? idk

Before these coursers, I could perform matrix multiplication and calculate the determinant of 2-3D matrices. I could just do it without knowing why it works and how to come up with that. These courses make me feel like I'm discovering math and proving to myself, like the first mathematicians maybe. I find myself saying:

So beautiful;
Of course! It's so logical and right there, how couldn't I see that?!
I could invent math in old times

Like in Computer Science now, we are used to work with abstraction over abstraction. So for me, these standard materials are like that. We are using abstraction to get the optimal results, but without looking deeper on how and why it works. Now we use transistors, python, DvD and etc etc. But these are the evolution of some base. And by studying this "base" (low level maybe), you'll get a much more profound knowledge (even if it is more time consuming)

And after all this, I now find myself remembering less, but deducting more and more until I remember a formula, following so a path of reasoning. It's like I don't need anymore to remember F=ma, because I understand enough to come up with it after a moments of thinking.

1 upvotes on reddit

notlfish · 3 years ago

FWIW math books are often in their problem sets as much, or even more so than in their main text (in fact, there are also wonderful problem books). You often won't get their beauty by reading them, but by working through them. I'm not implying anything about how you engaged with these linear algebra resources, just know that you could be judging fishes by their ability to fly.

2 upvotes on reddit

panzerfinder15 · 3 years ago

Watching 3B1B since Calc 1, he's awesome. Will check out the other vids!

Also recommend Krista King, she's great too!

11 upvotes on reddit

DumaDuma · 3 years ago

Has Krista king made linear algebra videos?

Edit: It looks like they are on her website behind a paywall. I may have to check them out

1 upvotes on reddit

panzerfinder15 · 3 years ago

Yup! I’m subscribed right now and find her vids and walk through a well worth the sections I’m struggling with.

2 upvotes on reddit

need_friends137 · OP · 3 years ago

Thanks for the tip, I will

1 upvotes on reddit

FeedMeMoreInternet · 2 years ago

Just going through the video course by 3blue2Brown and it's really a blast. I plan on following up with MathTheBeautiful. Thanks for the recommendation!

2 upvotes on reddit

need_friends137 · OP · 2 years ago

I'm glad my post was helpful to you

1 upvotes on reddit

teamsprocket · 3 years ago

Do YouTube courses include practice problems and tests?

3 upvotes on reddit

need_friends137 · OP · 3 years ago

Yes, but because there's no teacher to give it to you, you also have to search it yourself. And the more I do at least, the more I get better. It's like learning programming too. You start searching for projects and solving, until you move to a next subject. If it helps, here's the websites:

MathTheBeautiful

3Blue1Brown

But this is internet. You're learning for free, but YOU need to do the work that your teachers would do for you. You're on your own. But there's pleasure on keeping a schedule and whatever

1 upvotes on reddit

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r/GraphicsProgramming • [10]

Summarize

Linear algebra resources? I follow 3blue1brown, but struggling with Axler's "linear algebra done right"

Posted by dealingwitholddata · in r/GraphicsProgramming · 6 months ago

I'd like to really get the 'hang' of linear algebra so I'm confident in my spatial programming. I've used blender a lot and I seem to be comfortable with the concept of different types of vectors and spaces and using matrices to translate between them in my python scripts. Past that though, everything is very slippery.

I've cracked Lang and Axler, but I feel sorta over my head even in the first chapters. But the 3blue1brown videos are easy and tbh too simple. Surely there are some good resources 'in between'?

12 upvotes on reddit

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Tattva07 · 6 months ago

I would highly recommend this free ebook https://mathfor3dgameprogramming.com/

The chapters on linear algebra are very well done, in my experience. I hold a bachelor's in math and found lower division Linear Algebra quite challenging.

2 upvotes on reddit

wildyng · 6 months ago

The book you’re reading can be a little intimidating if it’s your first go at linear algebra and have little to no experience with proofs. To add, it’s hard to appreciate the ‘done right’ aspect of the book without having taken a previous course that teaches the concepts in a different ordering. I’d recommend looking into any applied linear algebra resources as that would most likely give you a better foundation. Haven’t read it, but just glancing over, “Applied Linear Algebra” by Olver looks promising and about the same style as the course I took at my university.

1 upvotes on reddit

trevorLG · 6 months ago

I took an intro course that used Linear Algebra and Its Applications by Lay, Lay and McDonald and thought it was quite a straightforward book with a lot of mechanical exercises. There are .pdfs. I have only worked through the SVD section of Linear Algebra Done Right but it seems difficult to get much out of it without having taken intro level proof-based coursework. Strang has other texts as well that I believe are more traditional but his authoring style isn't for everyone. A lot of the content in Linear Algebra Done Right is not useful for programming in the graphics pipeline unless you are getting somewhat esoteric.

2 upvotes on reddit

dealingwitholddata · OP · 6 months ago

Thank you!

1 upvotes on reddit

kozz76 · 6 months ago

I followed this course:
https://www.youtube.com/playlist?list=PL_a9tY9IhJuPDEDq97tq0uKXpsTZYBIXe

It has a very wide approach to LA, but it is useful for more fundamental understanding of its base concepts.

2 upvotes on reddit

dealingwitholddata · OP · 6 months ago

I will check this out

1 upvotes on reddit

GreatCosmicMoustache · 6 months ago

Coding the Matrix is pretty sweet, an implementation-first tour of Linear Algebra which doesn't skimp on the actual mathematics.

4 upvotes on reddit

dealingwitholddata · OP · 6 months ago

Awesome, thank you!

2 upvotes on reddit

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