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

Comments · 3.3K

• AK

  @akmalrazak9686 · 6 years ago

  Learning matrix in high school was like learning how to construct a sentence but never know it was for communication

  8.3K

• WE

  @wertnick86 · 7 years ago

  20 years after first being exposed to matrices, and getting a computer engineering degree, I finally understand matrix multiplication.

  4.4K

• ST

  @strengthinnumberstutoring61 · 4 years ago

  I have a degree in math and actually run a successful mathematics tutoring service. I have never seen anything like these videos. They are incredibly intuitive. Every time - every time! - there is some step where I say “oh, but you’re not paying attention to <b>this</b> detail or <b>that</b> detail,” within seconds Grant addresses exactly the misgiving I have by saying “now, it may seem like we’re being a bit dishonest here,” or some other welcome mixed dose of humility, honesty, and humor. Thank God for this channel - a rare glimpse into what it is like for mathematics to be considered a subject worthy of human inquiry.

  1.3K

• FR

  @frontmandylan2150 · 5 years ago

  This series is without a doubt the best educational content I&apos;ve ever come across on the internet. I can&apos;t thank you enough for these videos

  1.7K

• JO

  @josephvallillo1219 · 9 years ago

  I have a masters degree in engineering and this series is blowing my mind.

  5K

• JO

  @jojodasjojo · 1 year ago

  There where a lot of moment of me just being absolutely stunned by how intuitively you can explain the concepts!

  177

• FL

  @fluxtwee2804 · 7 years ago

  I love the small details like how Composition was colored to look like it is a composition of a rotation and a shear.

  631

• GR

  @GreenDayxRock1 · 10 years ago

  So for everyone else that had trouble with his &quot;honest to god proof&quot;... I&apos;ve taken a number of courses in linear algebra and many proof courses, and found the same hole in his explanation. Here&apos;s what he means though, he just left out a crucial intermediary in his proof:<br> <br>A(BC) means apply the overall effect of BC and then A. Of course, the overall effect of BC is equivalent to applying C then B based on what he explained earlier in the video. So we have just shown that applying the overall effect of BC and then A is the same as applying C, then B, then A. Similarly, (AB)C means apply C then the overall effect of AB. But applying overall effect of AB is equivalent to applying B then A. So we can just apply C then B then A and get the same thing. Since both A(BC) and (AB)C decompose to applying C then B then A, we have that A(BC) = (AB)C

  3.7K

• JU

  @JustaChillConlanger · 1 year ago

  <a href="https://www.youtube.com/watch?v=XkY2DOUCWMU&amp;t=576">9:36</a> color transfomation

  37

• RA

  @raviiit6415 · 8 years ago

  My ears feeling educated

  227

• AL

  @alfredwong1489 · 8 years ago

  &quot;Good explanation &gt; Symbolic proof &quot;<br>Exactly. I&apos;ve been screaming this in my mind every time I see math. If my middle school teachers taught like this I wouldn&apos;t have hated math.<br>Thank you so much :D

  394

• SE

  @Sentas9 · 3 years ago

  Our professor at our university in Germany suggested your YouTube channel to us because he couldn&apos;t properly represent the 3 dimensions on the board, and it has been very helpful to me. Thank you for your videos.

  55