Three-dimensional linear transformations | Chapter 5, Essence of linear algebra

What do 3d linear transformations look like?
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Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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[shinequashie]

I count myself as one of the luckiest people to have stumbled on this playlist just before taking linear algebra in college

[DekuStickGamer]

I never thought I'd say this but I stay late up at night to watch math videos. These videos are incredibly intresting and rich with decription and fluid animation.

[enricoiraldo]

I think the best way to use his amazing videos are:
1) watch his series on YouTube to get a general idea of the mathematical significance of the topic
2) study on manuals/uni the details and the exercises
3) re-watch to wrap up and abstract from details for a last consolidation

[KirillBezzubkine]

There s one special spot in heaven saved for you. For helping all those math-lost souls and shedding light on their minds

[AKSHAYKumar-gduq]

The composition of the two 3D matrices he shows near the end is
6-6-6 (top row)
33-44-55 (middle row)
6-10-14 (bottom row)

[dingo]

That feel when you've watched all the videos in this series the second they came out and can't wait for the next one to be released. Never been so stoked to hear how a person describes a determinant.

[jmiquelmb]

I had a little eureka moment when I realised that the identity matrix is the only transformation that won't change the position of the basis vectors. This series of videos is amazing

[atriagotler]

This series is a true masterpiece. I mean whole 3b1b is awesome, but this playlist just sits in a league of it's own.

This should be the gold standard for all linear algebra classes.

Also, linear algerba should be introduced much much earlier. It's not that complicated if explained in a common sense manner as you can see!

[danielrabinovitz]

I just want to genuinely thank you for saving me in my Linear Algebra class. Your style of teaching is extremely simplistic and fluid. I'm remembering why love math so much even when classes frustrate me immensely.

[markostojanovic]

Our linear algebra prof. always shares a link for one of your videos in this series at the end of every chapter in his skript because he is a big fan of your videos. I think that‘s great and we have a much better intuition for this topic, thank you!

[dynamicgecko]

I just now realized that the reason the identity matrix is a neutral element in matrix multiplication is because it is the default values for each basis vector (i, j, k, etc).
It transforms every vector back to itself. It makes so much more sense now! Man, this series is amazing. Thanks!

[marciomaiajr]

There's an old programming book titled "flights of fantasy". The author uses a lot of matrices for the 3d calculations and finally now, 20 years later, I understand why.

[seanm]

And now I understand identity matrices

[ExCoSeH]

Omg you deserve my money more than my teachers!! What is your PayPal??

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At this point in the tutorial, I just want to give you all my money. You've made my mathematics make so much sense, I feel like a child with an endless supply of candy!

[Cleisthenes]

All I can say is that if I were a mathematician, I would have three hats and call them i-hat, j-hat, and k-hat.

[teddybrow]

Five years after the initial release, I'm watching this series a third time around. It's a great refresher and a compelling watch every time. Thanks, Grant!

[djec-eazy]

Your ability to create fluid and intuitive animations to represent a topic is incredible and never ceases to add richness and clarity to a topic. Thank you for everything

[romanalaivi]

I forgot essentially all math from my school days. The way you explain this makes me realize there are actually many weak analogies to daily life and other tasks I've done like balancing a gimbal on each axis first. Amazing how intuitive this all is for someone whose forgotten just about everything and trying to get into machine learning. Thank you so much for making this so incredibly easy to understand. I feel lucky to have found these videos.

[bungeruwu]

Is that right?
6, 6, 6
33, 44, 55
6, 10, 14