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Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact.

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Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you’re into that).

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Xem thêm bài viết khác: https://batdongsancom.com/tong-hop

I don't who you are but I must say you are the "Einstien" modern era.

Sorry I don't really get the part on associativity. Why is it C->B->A for both examples? Doesn't the parenthesis for (AB)C mean that you should do B->A first then -> C?

Guy, you're incredible!

I can't be more thankful for the creators of this series. I am truly grateful.

hermano te amo, gracias por existir.

There are few who still misunderstood like me as follows: 1. Why commutativity is not satisfied, where as Associativity does satisifed by Matrix Multiplication. Just to make things clear, still ABC!=CBA. Its just A(BC)=(AB)C. In other words, on both sides of associativity, 1st transformation is C, 2nd Transformation is B and 3rd transformation is A.

Only in 2020, a brilliant guy who understands this shit is putting efforts to make it so lucid to everyone. I feel fortunate. The creator himself possible cannot imagine what kind of butterfly effect these teaching may lead to. Thank you so much.

I've only seen the first 4 videos in the series, and I've gained more valuable intuition than my semester long engineering linear algebra course. Thank you!

What you just taught here, it just blew me away. Never had I ever given thought to liner algebra in such a light. I am glad that i found this channel.

One suggestion, Please decrease your speed of explaining the concepts. It is a bit faster.

you are amazing

can you change the school system

Wow

This is the exact video I was looking for.

Linear Algebra review day2

Thanks bro, you are legend. Very helpful.

@3Blue1Brown: Grant, can we geometrically think of the special condition when matrix multiplication will be commutative? That is to say, under what type of transformations will the order of applying them not matter?

I didn't like the associativity proof. (AB)C is not applying C, then B and then A as written, despot being equivalent to such, but you stated it as if it was already proven to prove it. As written, it is the transformation C, and then the transformation that is (AB)

Oh I get it now

Multiplying two matrices has the same geometric meaning as applying one transformation then another.

Not quite sure on understanding i head and j head movement in the shear matrix. I see that it has to have does numbers in the shear matrix , but i don't understand how it is cooked up.

Simply fantastic job man, keep up the great work!

praiseworthy effort

very good

I do not like taking formulas for granted. So I came here for granted!

Jet Brains sent me here

wooo that matrices way of multiplication is really clicking !!

i really love it.

it make so much sense

why do we always have to multiply the transformation function matrux on the left? is it a convention or what? for a person who doesnt know about the rules of matrices and is trying to understand matrix as vectors, and its transformations, .. multiplying it only on the left doesnt make sense

Isn't it beautiful that feeling of finally understanding something that you've been speending a lot of time studying without any result?

I seriously think that this man's videos should be used in schools, or at least his method to teach students. It's wonderful !

Grant I always thought linear algebra to be a superb abstract concept,But you managed to find the intuition behind it,Its brilliant.

I don't understand shear transformation matrix . Please help me

谢谢!

What's the background piano sound???

Could somebody explain how we got the shear matrix at 3:20? I understand that their composition gives us the target matrix but how can I get this matrix in my mind?

Wow, you are the ultimate teacher.

I don't understand – at 7:34 he explains that order DOES matter, but then from 8:20 on he contradicts that and says order DOESN'T matter. can someone explain?