My lin alg prof quite literally believes that every 3blue1brown visualization instantly pops into every students head the first time they see a numbers stacked inside of [ and ]

Thanks for taking the time to make this... it is clear, concise and allows the watcher to really understand linear transformation.

Your videos on the Jacobian matrix are excellent. Clear, insightful and beautifully presented. Thank you.

3blue 1brown..... hey man it all makes sense.... thanks

Thank you sooooooo much. You are the best math tutor ever. Thank you for doing such a great job. Your videos are so helpful. They really make a big difference in my studies.

It could be convenient to address a possible confusion, for it would seem that in substituting the new, slanted grid for the old, we are not transforming e.g. (1, 0) into (2, 1), as claimed, but vice versa, since on the new grid, it is (1, 0) what formerly was (2, 1). I suggest: "note we are not changing the basis vectors so that the same old vector (1, 0) gets the new name (2, 1) but so that the same old name (1, 0) gets the new vector; this is required by the fact that L(x, y) = xL(1, 0) + yL(0, 1), that is, we must have the same quantities x and y of the transformed basis vectors L(1, 0) and L(0, 1)".

Man! I dont know who you are but that was truly enlightening .

For people who are confused: 4:05 the green vector in the deformed grid/world is DEFINED as [1,0] by people thinking/working with that grid! "We" multiply "their" understanding of a basis vector with the transformation matrix to translate their definition of a basis vector to our language where our basis vector look completely different! The transformation matrix helps us to understand that their definition of a basis vector like [1, 0] should be understood as [2, 1] in our definition of the world! If you wanna make "them" understand what "we" mean when we talk about a basis vector [1, 0] you have to multiply our (basis)vector with the inverse of the transformation matrix to translate "our" definitions of the world to "their" definitions of the world.

Random video in my feed, but now I'm interested :). On to the Jacobian, I guess.

Are you the 3Blue1Brown guy?

This voice makes me excited 😂

Thank you professor Khan

you are the best teacher.

Didn't realize this was Khan Academy until almost towards the end haha.

Very well presented!

What a lecture!

Question: why does the multiplication of two jacobi matrix, which are functions of one another, equal the identity matrix?

hell yeah i love this guy....is there a playlist of every video with this 3b1b dude

MORE MATH MAH BOIS!

This is absolutely beautiful ❤️

you are awesome, 3blue1brown

Great teachers, thanks ❤

Mind-blowing, pretty sexy graph explaining!

Covered this in calc 3 without linear algebra

what software is used for visualizing transformations?

KIDS just don't waste your time in school ...skip those classes and go swimming or play soccer..when you are home watch these videos.. Trust me, I wish I should have done that ,instead of wasting all those hours mugging up who knows what boxes full of numbers and derivatives.

Thank you

thank you so much

Shouldn't the first row of the matrix read " 2 1" and the second row read "-3 1". I am confused with why you conflated the x and y coordinates.

I really wish i'd seen this when i was actually taking linear algebra 😭

where is the next video?

so this is eigen vector and linear transfom I assume...

Did we just witness falling down the Golden Spiral? I noticed Fibonacci's sequence in your equations. Starting @ 3:07-ish *Edit - Pascal's Triangle as well, hmm?

THX!

Nice video, but did you ask 3Blue1Brown permission to use his animations?

Does anyone have the URL of playlist of this whole series? Thanks a lot.

Dope!

молодец, Я вас люблю

It's Grant....3Blue1Brown! I guess before he got famous.

Why 3blue... Is here?

Hm have a further nice journey. Tnx

Isnt this just the Gradient transpose?

what should I say.. god bless you

sounds like grant from 3b1b :D

He began to use Manim Cast

Ayyy its grant sanderson!!!

3 Blue 1 Brown guy, yes yes yes!!!!!!!!!!!!!

Jacobean was from the reign of King James.

Really better if you understand the linear algebra... But fair job anyway

cool

Grant I find you

dont know why people shower accolade on your explanation, it is messy and confusing.

69th video nice

wwoooooooowwwwwwww

I have watched over 100 Khan videos and this these are the first I have disliked. Using the 2 by 1 x, y matrix after the conversion matrix, is very confusing. It makes sense when you multiply by the basis vectors. Also flying the x y matrix to the left of the conversion matrix is really confusing.

🙏 Nothing Special..? 🪔