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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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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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36 COMMENTS

  1. 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?

  2. 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.

  3. 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.

  4. 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!

  5. 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.

  6. @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?

  7. 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

  8. 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.

  9. 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

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

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

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

  13. 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?

  14. 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?

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