Jacobian prerequisite knowledge
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- เผยแพร่เมื่อ 14 ก.ค. 2024
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Before jumping into the Jacobian, it's important to make sure we all know how to think about matrices geometrically. This is targetted towards those who have seen linear algebra but may need a quick refresher. - แนวปฏิบัติและการใช้ชีวิต
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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)".
Random video in my feed, but now I'm interested :). On to the Jacobian, I guess.
Very well presented!
Thank you professor Khan
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.
Are you the 3Blue1Brown guy?
He is!
Even I got the same doubt. but sir ur amazing really
you are the best teacher.
Man! I dont know who you are but that was truly enlightening .
3b1b
Great teachers, thanks ❤
What a lecture!
hell yeah i love this guy....is there a playlist of every video with this 3b1b dude
This is absolutely beautiful ❤️
MORE MATH MAH BOIS!
Didn't realize this was Khan Academy until almost towards the end haha.
This voice makes me excited 😂
thank you so much
Covered this in calc 3 without linear algebra
Mind-blowing, pretty sexy graph explaining!
Thank you
you are awesome, 3blue1brown
what software is used for visualizing transformations?
Question: why does the multiplication of two jacobi matrix, which are functions of one another, equal the identity matrix?
Do you know why by now?
THX!
I really wish i'd seen this when i was actually taking linear algebra 😭
Hm have a further nice journey. Tnx
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?
Does anyone have the URL of playlist of this whole series? Thanks a lot.
khanacademy.org
th-cam.com/video/VmfTXVG9S0U/w-d-xo.html
where is the next video?
Dope!
It's Grant....3Blue1Brown! I guess before he got famous.
what should I say.. god bless you
so this is eigen vector and linear transfom I assume...
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.
The landing spots for the basis vectors go in the columns, not in the rows.
молодец, Я вас люблю
He began to use Manim Cast
Ayyy its grant sanderson!!!
sounds like grant from 3b1b :D
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.
Why 3blue... Is here?
Isnt this just the Gradient transpose?
With rows for conponent functions?
Really better if you understand the linear algebra... But fair job anyway
3 Blue 1 Brown guy, yes yes yes!!!!!!!!!!!!!
Jacobean was from the reign of King James.
Nice video, but did you ask 3Blue1Brown permission to use his animations?
That is 3blue1brown
he won a contest of a khan ac. so yes. These lectures were made specially for K.A.
Be he IS 3Blue1Brown!
Grant I find you
cool
dont know why people shower accolade on your explanation, it is messy and confusing.
wwoooooooowwwwwwww
69th video nice
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..? 🪔