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.
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 RUclips 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: ruclips.net/video/0UvNF_cfBJ4/видео.html. You can contact me from my channel email: vizkernel@gmail.com .
@@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 !
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.
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..!!🙂🙏
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.
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!!
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. :)
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
Gahd damn this was cinematic. Loved the little details like the guitar strum starting from one note going to a full chord as you explained the completeness of SVD.
I just came across this video. Your explanation is absolutely amazing. Then I go to your channel and realise you haven't been on YT for 2 years. I wish you come back!
You have no clue how much this has helped me understand not only svd but also lin alg as a whole. I wish i found your channel sooner. You're very underrated, keep up the great work!
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.
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!
Your explanation of decomposition and svd is so impressive and effective to me. As you said, the insight you give from the video is so inspiring. Hope in future you can have the chance to finish this series. Thank you very much!
Come from another platform bilibili after watching a Chinese translated version. I have to say that this serie of video could be the best linear algebra visual interpretation. Thanks for delivering contents of such high quality.❤❤❤
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.
it's great!!! most of time, I can only know how to calculate and remember theoroms in my class. After watching these videos, i finally get what im learning this semester!
Wow! This takes 3B1B's style and does it better. I've always struggled to actually understand the intuition behind info presented in 3Blue1Brown's videos, but I was able to easily follow this video without even watching the first two parts. Granted, I have some background knowledge in symmetric and orthogonal matrices, transpose, etc. But this video took the things I could relate to from linear algebra class and combined them in a way that just... made sense. Bravissimo! the AoT jukebox music was also a nice touch:)
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.
I'm really enjoying the spawn of channels very similar to this and 3B1B. The animation style is something I missed during high school. I can also see that it's harder to make mistakes when you have and better fundamental understanding. Using this to solidify my understanding of my master's thesis.
watching all your videos on SVD gave me a feeling of watching an amazing series. it ends where it needs, every chapter is closed and you feel like you want more yet you know it was a correct time to stop. such a bitter-sweet feeling. Thank you!
Just guessing, I'm not the only one here never had a good understanding of SVD before this video, even though I had used it several times before. Please keep up the good work.
It is a phenomenal video! Building mental image of math object is so important for learning math and yours is really the best for this topic! I will recommend to anyone who wants to learn SVD!
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 🤤
I see what you did there with the AOT music at 11:20 during the reveal. Subtle. Nice. 9999999999999/10 video. Seriously. This might be THE best explanation of SVD
So many ways to explain SVD, yet so many instructions/instructors are about mechanics of svd offering no intuition or insight. This is the first time I saw svd developed using insight and intuition. I watched videos 1-4, repeatedly and thoroughly enjoyed it and now I can remember everything because the steps getting to why svd works are all intuitive. I look forward, sir, to your PCA lessons, been 2 years. Please?
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 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. :)
Prof. Strang would be proud, great work! Perhaps the one and only thing really lacking in his 18.06 course was the visual intuition behind all those transformations. You really can't give them justice on a black board only.
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
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!
Thanks for producing the video, it helps me to get a better understanding of SVD. While reviewing the lecture, I may spot a typo in the Visualization section as the following: 1. V^t rotate x from orthogonal basis V to standard basis 2. Σ scale and adjust the dimension 3. U then rotate from a standard basis to an orthogonal basis U Given the following formula and fact 1. Ax = (U Σ V^T) x 2. V^T is equivalent to V^-1 for orthogonal matrix Believe the sequence should be as the following? 1. V^t rotate x from standard basis to orthogonal basis V 2. Σ scale and adjust the dimension 3. U then rotate the result back to the standard basis Thanks again for the great video!
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.
Thank you for making the video. I find it very useful and engaging. Though it reminds me of 3Blue1Brown videos, you did an excellent jobs at covering topics that the other channel has yet mentioned. Wish you a lot of success to your channel.
Nice visualizations. Thank you for giving us a treat with such a big effort. Hope we deserve that. My objection: it was way too fast. These should've been two videos of 15-16 min each, covering the same topic. I had to pause every 3-4 seconds, even to read. The pace of the previous video (on spectral decomposition) was just right. I don't know for other people interested in this stuff, but I would love to see this broken down into two pieces with such convincing explanation as you did for the spectral decomposition, which was a real gem.
Omg There are some insights like wow adding dimensions!! I was following the algebraic procedure without knowing why, Thank you so much this was extremely helpful
omg, listening to this video while reading my notes and all of a sudden I hear made in abyss music, and i'm like no way, maybe another tab is playing? so then i immediately got to the info section and see it, thats awesome.
![NOSFERATU - Official Trailer [HD] - Only In Theaters December 25](http://i.ytimg.com/vi/nulvWqYUM8k/mqdefault.jpg)
The whole youtube math visualization comunioty needs to thank 3 blue 1 brown for inspiring a new generation of gifted people like yourself
100%
And for open sourcing his library for making these visualizations. (And the community who forked it, and now maintains it)
@@Dom-zy1qy Manim library?
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 RUclips 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: ruclips.net/video/0UvNF_cfBJ4/видео.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.
People like you will have a special place in heaven ❤
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.
This was super well done. Great job!!!
Thank you Vivek ! A very special "first comment" my video got here.
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.
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.
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..!!🙂🙏
Just went over all of these for my data science class, this deserves a million views. Thank you sir.
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.
I can't wait for the principal component analysis video you promised 👀
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!!
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. :)
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
Gahd damn this was cinematic. Loved the little details like the guitar strum starting from one note going to a full chord as you explained the completeness of SVD.
Thank you for explaining complex ideas in such an intuitive way! It has been immensely helpful to me!
I just came across this video. Your explanation is absolutely amazing. Then I go to your channel and realise you haven't been on YT for 2 years. I wish you come back!
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.
Awesome work! This is probably the best explanation of SVD on RUclips. Would be great if you created the PCA video
Amazing set of videos man! I don't have words to describe it! This is what the internet is meant for.
Not everyday do I come across videos on youtube that blow my mind like this one did. Cannot thank you enough!
You have no clue how much this has helped me understand not only svd but also lin alg as a whole. I wish i found your channel sooner. You're very underrated, keep up the great work!
These are fantastic videos. The intuition your animations instill is brilliant
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.
These 4 videos enlightened me more than the past two weeks of machine learning class
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!
Never seen such a detailed and great explanation of any topic. Excellent effort man. Keep teaching.
Your explanation of decomposition and svd is so impressive and effective to me. As you said, the insight you give from the video is so inspiring. Hope in future you can have the chance to finish this series. Thank you very much!
totally love it, I learnt 10X time more after watching this video than reading my book 10 times.
Beautiful. The comparison of the SVD to the Fourier Transform really cemented the ideas! Thanks.
This is terrific.... Extremely well explained a concept as complex as SVD. Thanks a lot.
After being bogged down with math for a while a visualization proof helps understanding very much, thank you
Come from another platform bilibili after watching a Chinese translated version. I have to say that this serie of video could be the best linear algebra visual interpretation. Thanks for delivering contents of such high quality.❤❤❤
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 four part series should be part of every linear algebra curriculum!
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!
it's great!!! most of time, I can only know how to calculate and remember theoroms in my class. After watching these videos, i finally get what im learning this semester!
Wow! This takes 3B1B's style and does it better. I've always struggled to actually understand the intuition behind info presented in 3Blue1Brown's videos, but I was able to easily follow this video without even watching the first two parts. Granted, I have some background knowledge in symmetric and orthogonal matrices, transpose, etc. But this video took the things I could relate to from linear algebra class and combined them in a way that just... made sense. Bravissimo!
the AoT jukebox music was also a nice touch:)
This video is a piece of art , just like the fancy world of math and linear algebra , thanks for the efforts !
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.
Super helpful, keep making more of these please 👌
I'm really enjoying the spawn of channels very similar to this and 3B1B. The animation style is something I missed during high school. I can also see that it's harder to make mistakes when you have and better fundamental understanding. Using this to solidify my understanding of my master's thesis.
I think the opposite about copying, I can praise innovation
watching all your videos on SVD gave me a feeling of watching an amazing series. it ends where it needs, every chapter is closed and you feel like you want more yet you know it was a correct time to stop. such a bitter-sweet feeling. Thank you!
Hope you had fun along the way !
Just guessing, I'm not the only one here never had a good understanding of SVD before this video, even though I had used it several times before. Please keep up the good work.
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.
It is a phenomenal video! Building mental image of math object is so important for learning math and yours is really the best for this topic! I will recommend to anyone who wants to learn SVD!
What a clear and honest video! Can't wait to see the next ones
Thanks bro !
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 🤤
This video is gold, I have watched several videos about SVD, but this one explained the best
You deserve to be remembered in my life.
meanwhile Gilbert Strang took weeks to teach this. you have done it in 17 mins. unbelievable pedagogical skills man. keep up the good work.
This video is a saviour.Thank you so much for such wonderful visualization. Please please please do more videos @visualkernel. Waiting for PCA
These 4 vedios are the best at explaining the matrices and the SVD , thanks a lot for your great effort
dude just: 1. talked about something that i needed to learn; 2. put in Shingeki music; 3. put in VSAUCE MUSIC.
You just gain one more sub my friend.
Come back and save more lives, man. Your videos have saved countless lives.
Awesome video thank you! Can't wait for your PCA video!
This should have way more views. Waiting for the next ones. Excellent!
I see what you did there with the AOT music at 11:20 during the reveal. Subtle. Nice. 9999999999999/10 video. Seriously. This might be THE best explanation of SVD
So many ways to explain SVD, yet so many instructions/instructors are about mechanics of svd offering no intuition or insight. This is the first time I saw svd developed using insight and intuition. I watched videos 1-4, repeatedly and thoroughly enjoyed it and now I can remember everything because the steps getting to why svd works are all intuitive. I look forward, sir, to your PCA lessons, been 2 years. Please?
Had SVD in controlsystems, and this video made me understand it so much deeper, thanks 👍
the visualization was very good and I just love the power and energy in your voice
A masterpiece! It was very helpful and now I feel like I know something huge. Thank you!
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!
Man, these videos are incredibly well made, good work. Also, I love the version of "My War" you played during the visualization :D
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. :)
Prof. Strang would be proud, great work! Perhaps the one and only thing really lacking in his 18.06 course was the visual intuition behind all those transformations. You really can't give them justice on a black board only.
literally coming back here a few times just to rewatch this, awesome video
Best linear algebra content on youtube BY FAR. Thank you!!
Man, this interpretation is divine level stuff. You are so good! Please make more such videos
Great job, looking forward for new videos- this is first video about SVD that actually clarified my understanding about it. Thank you!
This video is pure gold. More people should see it.
This is just magnificent…
What a phantastic series. Truly appreciate your effort!
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).
Finally, a both useful and beautiful, among just beautiful some2 videos.
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.
This video saved so much time, very well done! But i wasn´t expecting the crossover between Math and Aot.
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
Please continue doing videos man. Your teaching is great.
The 4 videos and the Attack on Titan Ost during the visualization as the final part was perfect. Thank you sir
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!
Great visualization of sequential roles of decomposed matrices!
"a video in the future" 🥹🥹🥹
Please more videos!!!
I was so confused with the SVD and your visulization really helps me understand!Thank you very much!
Thanks for producing the video, it helps me to get a better understanding of SVD.
While reviewing the lecture, I may spot a typo in the Visualization section as the following:
1. V^t rotate x from orthogonal basis V to standard basis
2. Σ scale and adjust the dimension
3. U then rotate from a standard basis to an orthogonal basis U
Given the following formula and fact
1. Ax = (U Σ V^T) x
2. V^T is equivalent to V^-1 for orthogonal matrix
Believe the sequence should be as the following?
1. V^t rotate x from standard basis to orthogonal basis V
2. Σ scale and adjust the dimension
3. U then rotate the result back to the standard basis
Thanks again for the great video!
This is art, it has been an exciting journey through lienar algebra. I really appreciate your job, thanks a lot !!!
thank you so much. This video was very helpful as I have been studying System identification and understanding SVD helped a lot.
Wonderfully presented man..come back and give us more!!
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.
Truly amazing video. Thank you very much.
Thank you for making the video. I find it very useful and engaging. Though it reminds me of 3Blue1Brown videos, you did an excellent jobs at covering topics that the other channel has yet mentioned. Wish you a lot of success to your channel.
Nice visualizations. Thank you for giving us a treat with such a big effort. Hope we deserve that. My objection: it was way too fast. These should've been two videos of 15-16 min each, covering the same topic. I had to pause every 3-4 seconds, even to read. The pace of the previous video (on spectral decomposition) was just right. I don't know for other people interested in this stuff, but I would love to see this broken down into two pieces with such convincing explanation as you did for the spectral decomposition, which was a real gem.
Omg
There are some insights like wow adding dimensions!! I was following the algebraic procedure without knowing why,
Thank you so much this was extremely helpful
omg, listening to this video while reading my notes and all of a sudden I hear made in abyss music, and i'm like no way, maybe another tab is playing? so then i immediately got to the info section and see it, thats awesome.
You are an amazing teacher making everything so easy to understand.
Man ! Please explain PCA the way you explained SVD , magical ....