SVD Visualized, Singular Value Decomposition explained | SEE Matrix , Chapter 3
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- čas přidán 2. 06. 2024
- A video explains Singular Value Decomposition, and visualize the linear transformation in action.
Chapters:
0:00 SVD Intro
1:17 Visualize a Rectangular Matrix ?
5:16 Creating Symmetric Matrix
7:17 Singular Vectors and Singular Values
8:55 SVD Formula Dissection
10:05 The Visualization
12:54 Is this SVD ?
15:16 The Next Journey
Video Sins:
1. Regarding the eigenvectors of symmetric, it is correct to say the eigen vectors are orthogonal if the matrix is full rank. However, the formal definition is there always exist a orthornormal basis which contains the eigen vectors of the symmetric matrix, for details refer to • 25. Symmetric Matrices... , where professor Strang explains the case with eigen vectors with eigen value of 0.
2. When S_L or S_R right has eigen values of multiplicity more than 1, there is an entire subspace of them, therefore, we need to put an orthonormal basis of the subspace to sure all the eigen vectors are perpendicular. Of course, this is already getting more involved with the details with the derivation of the SVD formula in the first place, I think I will leave this to the expert: • 6. Singular Value Deco...
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...
Music Credit:
1. Lord of the ring lofi by Sam Cisco: • Lofi of The Rings - Lo...
2. "First Layer" ost from an anime called Made In Abyss
3. "My War" lofi from AOT, music made by Kijugo • my war (Attack on Tita...
The whole youtube math visualization comunioty needs to thank 3 blue 1 brown for inspiring a new generation of gifted people like yourself
People like you will have a special place in heaven ❤
Not everyday do I come across videos on youtube that blow my mind like this one did. Cannot thank you enough!
I never thought in my life that I'd watch a linear algebra matrix video with the same interest as the real Matrix movie
so true dude
WOW! You have an extremely rare gift. I'm at a loss for words. I love 3Blue1Brown and Prof. Strang. But you just took pedagogy to a whole different level. This is unbelievable!
I watched all four videos in one sitting. I understood things I've tried to understand for years.
I'm not kidding I have tears dripping down my cheeks right now.
I hope you make more videos.
Thank you thank you thank you!
I never leave comments.
meanwhile gibert strang took weeks to teach this. he has done it in 20 mins. unbelievable pedagogical skills man.
After 10 years of struggle I can finally understand SVD. Congratulations Sir!
These 4 videos have been a real treat. You have a gift for simplifying complex ideas. Hope you find time to continue making videos. As you said with one of the video quotes - this animation wasn’t even possible until recently. Every one I talked to that learned Linear Algebra before CZcams thinks of it as a boring abstract, useless (!) area of math. It’s wonderful to see it come to life by generous educators like you. Please continue to contribute as time allows. I would love to see your take on the General Stokes Theorem and metric tensors! Is there a way to contact you directly?
Hi John, thank you for your patience sitting through all 4 videos, I actually believe most people who watched SVD never even know about the existence of the previous chapters. I am actually not a math major student, so I will defer your question about General Stokes Theorem to this channel: czcams.com/video/0UvNF_cfBJ4/video.html. You can contact me from my channel email: vizkernel@gmail.com .
Higher level Math is often written in a bland and uninteresting way when it is far from that. You Sir, have brought life to the topic. Blessings!
@@visualkernel This gorgeous episode made me realise there are previous chapters to it, I will definitely watch all of them despite I already learnt those topics but I am still interested in your versions, I know they would still bring me some new insights !
Bro u r just amazing. This is outstanding.
It's hard to pay attention when you recognize all the anime songs😂 good job either on SVD and sounds!
After searching the entire Internet for whole day, I bumped into this series which gave me clear visual interpretation of what and why of SVD to understand PCA, free of cost far better than paid ones. Without this, these algorithms are just numerical operations making no sense to any individual not expert in Algebra and all.
You are a pure boon and bliss to learners like us. Such beautiful work are another dimension to humanity. Thanks a lot..!!🙂🙏
After many days in the desert of linear algebra, thank you for teaching us how to ride those horses and helping us understand their names.
This was super well done. Great job!!!
Thank you Vivek ! A very special "first comment" my video got here.
Came here from the peer review!
This is very well animated and well motivated in the beginning. A hard agree on that matrices can have wildly different meaning in different contexts. Just a bit of nitpick at the end - I don't think Fourier transform works for ALL functions, just sufficiently "nice" functions (while SVD really works for ALL matrices). I understand the comparison being that they are decomposition of some "complicated" objects into "simpler" objects to deal with, though. But anyway, this is a very good video!
DAMN !!! Mathemaniac is peer reviewing my video ?! What a honor ! I think you are right, fourier transform really doesn't work on ALL function. By the way, I think your Quintic video is going to win this year, it's so impressive.
I can't wait for the principal component analysis video you promised 👀
my god dude, you are incredibly gifted. I didn't have to squint my eyes to understand everything. Very articulate and powerfully simple. Thank you.
This is by far the most brilliant and entertaining videos for understanding linear algebra. You've done a very great job man! Thank you so much.
Great job, looking forward for new videos- this is first video about SVD that actually clarified my understanding about it. Thank you!
Awesome work! This is probably the best explanation of SVD on CZcams. Would be great if you created the PCA video
This video series was fantastic. It does a great job explaining everything that leads up to the SVD. I tremendously look forward to any more videos from you. :)
Thank you for explaining complex ideas in such an intuitive way! It has been immensely helpful to me!
"a video in the future" 🥹🥹🥹
Please more videos!!!
8:59, I can feel when you speaking the equation, you are as excited as performing Kamehameha accumulated on your hands for so long. Your video is awesome bro!
Absolutely brilliant! Very very good presentation, the editing, aesthetics and overall effort you put into these is phenomenal! Please please continue making them :)
I was very demotivated to study for my final and this boosted my motivation a lot and made the entire course so much super intruiging. I now constantly think to myself, what does this really mean visually and it helps a lot! Thank you!
This should have way more views. Waiting for the next ones. Excellent!
A huge thanks. You deserve the Oscar for "Best Matrix Algebra Teacher" for this (together with Chapter 1 & 2)! ..... a real achievement in describing a difficult set of concepts in such an intuitive visual manner. Congratulations!!
This is the best visualization I have ever seen on a plethora of topics in Linear Algebra. Thank you! Eagerly waiting for the next video from you.
What a phantastic series. Truly appreciate your effort!
Come back and save more lives, man. Your videos have saved countless lives.
This is terrific.... Extremely well explained a concept as complex as SVD. Thanks a lot.
Awesome video thank you! Can't wait for your PCA video!
Absolutely beautiful my man! Brought me to tears. The most ingenious part was introducing the dimension eraser/adder. After that, everything was smooth as butter.
This video was so good what the hell. Thank you for the effort you put into it and thank you for uploading such high quality content for free! I think you just saved my semester
This is art, it has been an exciting journey through lienar algebra. I really appreciate your job, thanks a lot !!!
A masterpiece! It was very helpful and now I feel like I know something huge. Thank you!
Beautiful. The comparison of the SVD to the Fourier Transform really cemented the ideas! Thanks.
I was so confused with the SVD and your visulization really helps me understand!Thank you very much!
Great and super fun ways to learn these concepts. Your videos are life saver! It would be so great to have PCA explained as well. Thank you!
Man, this interpretation is divine level stuff. You are so good! Please make more such videos
This was very helpful for understanding SVD, thank you so much! I'd love to see more video's from your channel in the future.
These videos are, in my opinion, best explanations ever to linear algebra and matrix decompositions. I have watched tons of videos and read two books. None of which gave me intuition about linear algebra, only formulas and I couldn't get my way out of it.
Thanks. Please, keep making videos like this.
Best linear algebra content on youtube BY FAR. Thank you!!
Great video; made me want to watch your previous videos, as well. hope to see more from you again soon.
Very good! You have the perfect balance of talk and graphics. Excellent work!
I would love to see all those weird other factorizations (like triangular, Cholesky, blah blah) in your excellent visual demonstrations!
what an amazing explanation. Thank you!
What a magnificent explanation, thanks a lot!
This is absolutely mind blowing. The way you can explain these concepts visually and intuitively is beautiful and clear. I should not be able to watch this for free
in before this blows up. I noticed made in abyss ost, lol it's nice thinking music.
I am just more than surprised by how cultured a SVD video's audience can be. (I am just a first layer kinda guy).
Really exceptional work. Like you said, it's amazing that we have the opportunity to learn like this (special shout out to Manim, the free, open source software used to make these animations). You're doing a huge service to thousands of people.
I am gonna remember these concepts for the rest of my life - all because your videos provided an intuitive insight which cannot be any simpler. Hats off! SVD always scared me, but far less now. :)
Had SVD in controlsystems, and this video made me understand it so much deeper, thanks 👍
Amazing!! This is so elegant!! Thank you sooo much!!
This video is pure gold. More people should see it.
Man, these videos are incredibly well made, good work. Also, I love the version of "My War" you played during the visualization :D
Great videos and complement to 3B1B. Thanks!
Thank you for this amazing peace of work. I want to let you know that you helped me to understand this topic. This is by far the best explanation I 've seen here.
Thanks for another point of view in SVD my friend! I'm really appreciated.
Never seen such a detailed and great explanation of any topic. Excellent effort man. Keep teaching.
Saw your all videos, Thanks so much for your beautiful awesome visualization. It helps a lot!!! Looking forward to your next video about PCA , Thanks !
Phenomenal. Great presentation and mastery of manim, thank you.
This four part series should be part of every linear algebra curriculum!
I hope your channel blows up. This was great
Great video thanks for taking the time to make it. Really helpful
Just went over all of these for my data science class, this deserves a million views. Thank you sir.
very interesting and useful series of videos!
Amazing series of videos, keep em coming!
the visualization was very good and I just love the power and energy in your voice
Keep up the good job, do not stop doing videos, they are a bless...
You are an amazing teacher making everything so easy to understand.
I see now... Thank you very much, been struggling with doing PCA using this but now I know. And I'll be waiting for the video of PCA!
This is beautiful. Thank you!!
Excellent work. Keep it up !
Brilliant visualisation man , thank a lot.
You deserve to be remembered in my life.
This video is gold, I have watched several videos about SVD, but this one explained the best
literally coming back here a few times just to rewatch this, awesome video
Thank you kindly for this explanation and all work you've performed to make this material.
Finally, a both useful and beautiful, among just beautiful some2 videos.
learnt so much from this series, thanks!
This was a truly epic video.
Wonderfully presented man..come back and give us more!!
Super helpful, keep making more of these please 👌
These videos are awesome! Please continue and thank you so much
Top range videos I've ever seen in my life, plz keep doing them. It really helps someone who is learning linear algebra. Thank you so much.
Impressive! Love the way you teach! Thanks a lot for the awesome content!
this was amazing, great job!
Great visualization of sequential roles of decomposed matrices!
These videos are excellent. Very rare to see an explanation that reveals the intuitive and REAL meaning of these processes and not just a bunch of equations. The most important thing is to understand what concept.
The moment you realize the music in the background is the first opening of attack on titan s4, hilarious. Incredible videos BTW, keep going
Good God, this series is extraordinary ! Thank you
Thank you sooo much for making these videos. They inspire me a lot!
Please continue with those videos, they are very well done ❤
An absolute effing treat this seres has been. Youve explained SVD better than people who have written books about the subject. So gifted, thank you for sharing. Cant wait to see the next video promised 🤤
After being bogged down with math for a while a visualization proof helps understanding very much, thank you
Oh my gosh, this is INCREDIBLE!!! Thank you so much! 😍🤩
Please continue doing videos man. Your teaching is great.
thank you for this amazing video!
I learned so much. Thank you!!!
What a impresionated video, keep going, you are absoluty awesome !
YES ANOTHER 3 BLUE ONE BROWN!!! WE NEED MORE AWESOME MATH VISUALS!!!!
Great video! Looking forward for PCA!
These 4 videos enlightened me more than the past two weeks of machine learning class