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Matrix multiplication as composition | Essence of linear algebra, chapter 4

admin by admin
June 5, 2020
in Tổng Hợp
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Matrix multiplication as composition | Essence of linear algebra, chapter 4



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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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Comments 21

  1. jie situ says:
    3 years ago

    This series is simply awesome. I got engineering master, and working in quantitative finance now. Lots of matrices during my study and work. However, I never understood how people came up with this kind of method. When I was in college, I had no idea why we need to learn this. After this series, every dot are finally connected. Thank you, and, hats off to all those great great mathematicians. What we are enjoying now are all based on their great and genius work hundreds of years ago.

    Reply
  2. Muhammad Awais says:
    3 years ago

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

    Reply
  3. rafeang says:
    3 years ago

    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?

    Reply
  4. Олексій Ігнатенко says:
    3 years ago

    Guy, you're incredible!

    Reply
  5. Kshitiz Bohara says:
    3 years ago

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

    Reply
  6. Arbey Londoño says:
    3 years ago

    hermano te amo, gracias por existir.

    Reply
  7. Hari Sridharan says:
    3 years ago

    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.

    Reply
  8. Rituraj Borah says:
    3 years ago

    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.

    Reply
  9. Russ Goetz says:
    3 years ago

    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!

    Reply
  10. Pranay Bahuguna says:
    3 years ago

    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.

    Reply
  11. Kumar Vaibhav says:
    3 years ago

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

    Reply
  12. Mrxc Max says:
    3 years ago

    you are amazing

    Reply
  13. Mrxc Max says:
    3 years ago

    can you change the school system

    Reply
  14. Henson says:
    3 years ago

    Wow

    Reply
  15. Tan Soon says:
    3 years ago

    This is the exact video I was looking for.

    Reply
  16. Quitest says:
    3 years ago

    Linear Algebra review day2

    Reply
  17. John Hammer says:
    3 years ago

    Thanks bro, you are legend. Very helpful.

    Reply
  18. Anant Chopra says:
    3 years ago

    @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?

    Reply
  19. IndustrialDonut says:
    3 years ago

    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

    Reply
  20. Mostafa Flaifel says:
    3 years ago

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

    Reply
  21. Ron nooyer de says:
    3 years ago

    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.

    Reply

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