Visualize Different Matrices part1 | SEE Matrix, Chapter 1
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- Опубликовано: 31 май 2024
- Visualizing, identity matrix, scalar matrix, reflection matrix, diagonal matrix, zero matrix, shear matrix, orthogonal matrix, projection matrix, inverse of a matrix.
Chapters:
0:00 Visualize Matrix, but how ?
3:07 Identity Matrix
4:02 Scalar Matrix
6:23 Matrix in 3D
7:01 off-one Matrix
8:45 Reflection Matrix
10:54 Diagonal Matrix
14:00 Zero Matrix
Hopefully providing more intuition about matrix transformation on vectors and making the very abstract object of matrix, more relatable to us. This visual approach to matrix transformation also is the foundation to the Grand Finale of visualizing SVD.
This video wouldn’t be possible without the inspiration of the legendary 3b1b :
/ 3blue1brown
and the animation software - Manim, which he wrote:
/ 3blue1brown
and the Manim Community:
docs.manim.community/en/stabl...
Video Sins:
1. 1:16 I said “ we should think what happens to all vectors, as each everyone of them gets multiplied by the matrix “. I think my statement is factually incorrect, you can understand everything about a matrix if you know how it acts on the basis, i,j,k vectors. See the www.youtube.com/watch?v=kYB8I.... It’s a personal decision to put more vectors/arrows/dots/ on screens, because I think it increases our cognition to interpret the matrix, such as shearing, scaling, rotation transformation just becomes very visible. I also think this facilitates a very smooth transition to matrix transformation on pictures.
2. Sorry for calling identity matrix ‘boring’, it’s perhaps the most special matrix that there is. Consider every other matrices that exist does some transformation on vector, the identify matrix is the only one that does nothing. Many proofs in Lin Alg actually relies on assistances of identity matrix.
3. 5:40, I said “shape is just infinite number of dots sitting very closely together”. Sorry for using the word infinite so lightly, ... you get the idea. If I were to be more formal, I should have said a shape is collection of vertices sitting closely together: math.hws.edu/graphicsbook/c3/... .
4. Whenever it said “scale x axis by 3” on screen, it’s the lazy way of saying stretching vectors longer by factor of 3 purely in the x axis direction (horizontal direction).
Image Credits:
super mario, nyan cat, crypto punk, plants vs zombie-peashooter, and Obito
omg this is so underrated, probably the best intro out there
this video is on comparable level with 3blue1browns video, I hope you continue doing these.
the idea was even unique and precisely represented
Genius. If this is the way linear algebra is taught, everyone will love it.
I wish I had a time machine and could show this to the younger me. That way I could become good at these stuff and build the time machine!!
Dear old bootstrap paradox.
Am 16 now is it late
school and college passed thinking matrix world are just collection of numbers with some rules, while trying to learn linear algbera for machine learning , got to see these videos , it's not just number , its so intresting. wow nice, bravo to the author.
I see what you did @ 13:04 , playing single note for single transformation, then a chord composed of the notes for the combined transformation ✨
I loved this video. I'm currently self learning matrices and linear algebra for ML and this massively helped me understand. You really do feel similar to 3b1b's teaching style, the content flows well. Thank you.
W h y is this video not popular already??
The animation and the humour is so good
I love it :D 🖤
At 13:56, what notes are you using? With this matrix multiplication idea, you could convey the concept of 1st and 2nd inversion chords, i.e., slash chords ( using |R 3x3 matrix eg Cmaj/E or Cmaj/F etc.). Please let me know if I am wrong. Again exciting idea, I never thought of music that way! Great stuff!
Very well put and animated.
I'm currently studying a Masters in Applied Math and I had never seen these concepts so clearly explained. Your channel should be bigger.
very cool. I knew this already but visualizations you are making are really intuitive and just awesome. Thank you for doing this)) Scaling along Y axis was fun by the way)))))
Did you check out spectral decomposition and SVD? Those are pretty fun too.
Great video! Appreciate the effort!
Which software do you use for visualization?
Making Obito disappear by using the zero matrix was just genius! And that the origin was in his eye was the cherry on the cake! Thank you very much for the great video. It helps a lot to strengthen the understanding of what a matrix can do and why it is built the way it is.
i noticed too hahaha what a nostalgic moment
Excellent use of graphics! Makes everything clear.
Absolutely brilliant video, it is filled with so many insights and aha... moments. Going to watch all the four videos now!!
Great work! it's very useful, thank you so much
Just perfect, now Linear Algebra is getting make sense. Thank you! 😊
This is a fantastic video, and beautiful animations and explanations
Wonderful video, thank you for the effort!
Really COOL, thanks for your efforts
Awesome visuals! I'm subscribing :)
Really enjoyed the vid!! ur really underrated
Such a great course. Now I can really say I understand a little about matrix. I was in a mess with the matrix before.
So coo! Love it❤
😱 It's great to find this kind of videos.
Thank you - that is awesome. Really, really awesome.
Very useful. Thanks for the effort.
extremely underrated!
Amezing video. Thank you very much sir❤
I loved your video please consider making mini series like this if you have a time❤
Legend video
Thank you for the informative video.
These videos are great! I’m reviewing matrices for a computer vision class. And I like the humor. Thank you!
Sir no words are sufficient to hail ur good job❤
That's brilliant!
Thank you so much!
Excellent!!
Great video!
Brilliant!!
sublime
This really helps
I prefer the graphics on this one better thsn 3b1b, because its simpler. I find the transformation graphics in 3b1b very confusing. I prefer this one. Whoever made these videos havent mentioned their names though to thank.
hope for more videoes.Thank u
Thanks!
How visualize a 4×4 matrix multiplication with a vector?
nice video!!
Great!
This is cool
Your link in the description to 3blue1brown's third episode is faulty. Either correct the link or refer by name.
Also, very nicely made video! Underrated channel.
please make more videos like this! before u know it, number of subscribers skyrockets
I always told people to visualizee math. It's hard to remember or understand what you do when only writing numbers.
Nice Music!
Brother which animation app u used
Idk what SEE means. But I like to think it means “summer of exotic excursions”
The anime references (yes that includes the bellsprout) are a slick touch 😁
Oh, that Bellsprout was a Peashooter.
From "Plants Vs. Zombies", a classic game in game design.
In case it wasn't a joke, I'm commenting to suggest checking it out: it's a quite good simple and accessible game.
The Obito disappearing on his own open eye as point-zero was surely interesting.
i like ur channel better than threeblue1brown
broooooooo why u only have 4 videos
Please make more videos
Amazing video! +1 for the cryptopunks xD. Came across your video while doing spectral analysis on erc20 token tranfers. :)
I Think the name if the third is the stretch matric
I love with shape of maths.....ooo aa ooo aa ooo aa...oooooo
wow man you kick ass
Affine tranformation explained well! More fun than 3b1b like example the use of pokemon images a objects 😂
Oh, that Fictional Plant Monster wasn't a literal Pokémon. It was from "Plants Vs. Zombies", a classic game in game design.
In case it wasn't a joke, I'm commenting to suggest checking it out: it's a quite good simple and accessible game.
Background music distracting
nooo obitoooo
10:25 it sure is cool to check on pixelate drawings,
and apologies to unhealthy practices sure is Not cool.
Nowhere near cool.
So may we health care, sir. Learning: it is way past cool.
all these dots are…. pointless. Its enough to focus on the basis vectors and the square / cube it spans