Ask HN: Best beginner friendly linear algebra book?

		Ask HN: Best beginner friendly linear algebra book?
	22 points by belfalas 42 minutes ago \| hide \| past \| favorite \| 20 comments
	Hello all, the title really says it all. Hoping to find a linear algebra book that is friendly for visual learners.

I have a text at https://hefferon.net/linearalgebra/index.html. It is aimed at beginners. It comes with perhaps two dozen exercises per lecture along with complete worked answers to every question, along with videos of the lectures, a lab manual using Sage, and some other ancillaries.

Like others here I recommend 3B1B, which may be what you are looking for visually, but whatever you end up with it is absolutely crucial that you do exercises. Do many of them. It is the only way to get better.

Although it’s not a book, a good series on YouTube is 3Blue1Brown Essence of Linear Algebra. That explains it in a very visual way. That, in addition to Linear Algebra and its applications by Gilbert Strang, would be a strong mix. I would also recommend 3000 solved problems in Linear Algebra by Seymour Lipschutz as a strong foundation in linear algebra requires practice.

Essence of linear algebra is an absolutely wonderful series. It gave me an intuition of the subject in a matter of hours in way years of university didn’t do.

https://youtu.be/fNk_zzaMoSs

Why are you trying to learn linear algebra?

This is highly important. Linear algebra is applicable to so many fields, but learning linear algebra for say... Graphics Programmers, is a completely different feel from learning linear algebra for an Electrical Engineer Signals-and-systems engineer.

Graphics programmers largely need to learn "how to use" matricies. Emphasis on associative properties. Emphasis on non-communitive operations.

In contrast, Electrical Engineers / Signals-and-systems want to learn linear-algebra as a stepping stone to differential calculus. In this case, you're going to be focusing more on eigen-values, spring-mass systems / resonant frequencies, applicability to calculus and other tidbits (how linear algebra relates to the Fourier Transform).

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The graphics programmer (probably) doesn't need to learn eigenvalues. So any textbook written as "linear algebra for graphics programmers" can safely skip over that.

The electrical engineer however needs all of this other stuff as "part" of the linear algebra class.

I'm sure other fields (statistics, error-correction codes/galois fields, abstract algebra, etc. etc.) have "their own ways" of teaching linear algebra that is most applicable to them.

Yes, "linear algebra" is broadly applicable. But instead of trying to "learn all of it", you should instead focus on the "bits of linear algebra that is most applicable to the problems you face". That shrinks down the field, increases the "pragmatism" of your studies.

Later, when you're more familiar with "some bits" of linear algebra, you can then take the next step of generalizing off of your "seed knowledge".

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I personally never was able to learn linear algebra from a linear algebra book.

Instead, I relearned linear algebra 4 or 5 times as the "basis" of other maths I've learned. I learned it for differential calculus. I relearned linear algebra for signals. I relearned linear algebra for Galois fields/CRC-codes/Reed Solomon. I relearned linear algebra for graphics.

Yes, it seems inefficient, but I think my "focus" isn't strong enough to just study it in the abstract. I needed to see the "applicable" practice to encourage myself to learn. Besides, each time you "relearn" linear algebra, its a lot faster than the last time.

Personally I liked the No Bullshit Guide to Linear Algebra. It kind of builds up things slowly and in a conversational manner, but you can also skip thru pretty quickly if you just need a reference.

I don't think I've been able to find any particularly good visual LinAlg books - most of what you're trying to achieve is actually quite abstract and I found the classic books a little confusing.

As an addendum - if you live stateside, classes at community colleges may be quite inexpensive and fairly approachable.

Second to No Bullshit Guide to Linear Algebra. It's well written, has plenty of practice problems, and an interesting applications section.

Fun series on learning practical linear algebra from a robotics engineer: https://youtu.be/FKs1XhlrZDw

I don't remember how I found this guy but watching him feels more like learning from a friend who's extremely knowledgeable about linear algebra rather than sitting in a university course.

“Introduction to Linear Algebra” by Gilbert Strang is the book. Recommend getting a used older edition as not much has changed.

His course at MIT is legendary, completely available online https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010...

And there’s so much good linear algebra stuff on YouTube from 3brown1blue.

If you can do one thing now, watch this Veritasium video to disprove the myth that you’re a visual learner: https://youtu.be/rhgwIhB58PA.

Also, Khan Academy is an excellent supplement for parts you find confusing.

Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares : https://web.stanford.edu/~boyd/vmls/

I’d ask a follow-up question of: what are the prerequisites for being able to successfully complete any of these courses/books? I’ve been thinking of doing something similar myself, and am 20 years removed from daily math exercises. Thanks in advance!

Try Singh's _Linear Algebra: Step by Step_, along with youtube.

Higher math tends to be abstract; you can't visualize higher-dimensional linear algebra concepts directly. The standard resources (Strang, Axler, etc) are worth the effort.

I really liked Linear Algebra And Its Applications by David C Lay, although it seems that more people dislike it. I believe it's a pretty common book for college intro courses. It does illustrate everything pretty well if I remember correctly.

Perhaps a game development book is even more visual? I haven't read it (yet), but this book is getting recommendations: https://gamemath.com/book/

I recommend The Manga Guide to Linear Algebra! I read it the summer before college and their visuals and analogies really helped me grasp basic concepts.

I disagree. I personally found that one to be a poorly written "Manga Guide". (Manga Guide to SQL was a good one, but there really weren't as many good analogies for Linear Algebra).

A lot of the "examples" were "This is complicated and abstract, so we'll just say it is and go to textbook form".

What are you learning for? I'm in the industry learning for work in medical image visualization.

If you want something hands on: "coding the matrix"

I’ll second this book, tons of very practical exercises to help you understand what’s happening for every main concept.

Nothing holds a candle to https://web.stanford.edu/~boyd/vmls/

Applied learning is the best way to learn linear algebra.

Recommend

Getting started with linear algebra

Linear Algebra Essentials with Numpy (part 1)

GitHub - yizhen20133868/MIT-Linear-Algebra-Notes: Notes for MIT-Linear-Algebra

Linear Algebra of Types

The Linear Algebra Mapping Problem

Linear Algebra Basics: Dot Product and Matrix Multiplication

Computational Linear Algebra for Programmers (2017)

Linear Algebra for Data Scientists — Explained with NumPy

An Intuitive Guide to Linear Algebra

什么是线性代数(linear algebra)?- 产品经理的人工智能学习库

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