SVD Visualized, Singular Value Decomposition explained | SEE Matrix , Chapter 3

[@bananalord8575]

The whole youtube math visualization comunioty needs to thank 3 blue 1 brown for inspiring a new generation of gifted people like yourself

[@CraszyAsce]

100%

[@Dom-zy1qy]

And for open sourcing his library for making these visualizations. (And the community who forked it, and now maintains it)

[@Physics22KU]

@@Dom-zy1qy Manim library?

[@molackanil4115]

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.

[@AamirAliDrigh]

meanwhile gibert strang took weeks to teach this. he has done it in 20 mins. unbelievable pedagogical skills man.

[@zenicv]

I never thought in my life that I'd watch a linear algebra matrix video with the same interest as the real Matrix movie

[@RasberryPhi]

so true dude

[@PriyanshuSinhasc]

Real matrix movie was cringe

[@artophile7777]

​@@PriyanshuSinhasc ok

[@MrGameface123]

Haha, so true

[@marcelogranja]

After 10 years of struggle I can finally understand SVD. Congratulations Sir!

[@johnstuder847]

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 KZbin 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?

[@visualkernel]

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: kzbin.info/www/bejne/ZobZf3mVmMt1gJY. You can contact me from my channel email: [e-mail] .

[@stefanfarier7384]

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!

[@exoticcoder5365]

@@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 !

[@karthikrajeshwaran1997]

Bro u r just amazing. This is outstanding.

[@peilanhsu]

Awesome video thank you! Can't wait for your PCA video!

[@whiteduck5563]

this is the most basic and understandable explanation about SVD on KZbin. nice job

[@preetysingh7672]

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..!!🙂🙏

[@suman14san]

People like you will have a special place in heaven ❤

[@vcubingx]

This was super well done. Great job!!!

[@visualkernel]

Thank you Vivek ! A very special "first comment" my video got here.

[@MrRykooo100]

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.

[@saleemun8842]

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.

[@mathemaniac]

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!

[@visualkernel]

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.

[@gaytrisachdeva7544]

I am so happy after watching this, the kinda happy you feel when you finally understand something, you are sensing there is a pattern to all this maths i am doing and those dots finally connect. I hadn't felt that in a long time. Thank you so much for the efforts. I am just intellectually satisfied today.

[@htetaung04]

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!

[@basedland]

Just went over all of these for my data science class, this deserves a million views. Thank you sir.

[@francoisvictor8]

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.

[@marcoparco_9564]

one of the best animated math videos i have ever seen! You earned yourself a new subscriber

[@markclintworth6134]

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!!

[@ai_station_fa]

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.

[@pengqianlu6824]

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!

[@institv7733]

I really can´t thank you enough for doing this video series, it helped me a lot to continue my linear algebra learning journey, I hope you are doing great and I hope you consider doing more videos like this in the future.

[@louwang1803]

dude, also a fan of 3B1B here, you need to know how amazing you are as well, thank you so so much

[@cs02421]

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. :)

[@DanielaGonzalezdelaGarza]

Thank you for explaining complex ideas in such an intuitive way! It has been immensely helpful to me!

[@RajatRaj-o3v]

Teaching hardcore Linear Algebra visually, while playing 'My War' from 'Attack on Titan' in the bg, you have crossed the heights of greatness, my buddy

[@shivc22]

Awesome work! This is probably the best explanation of SVD on KZbin. Would be great if you created the PCA video

[@jonathanliu4201]

These are fantastic videos. The intuition your animations instill is brilliant

[@dmitryr9613]

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:)

[@pine_9356]

Wow, I just binged the whole series You've unlocked a new emotion for me: being excited about math! Or perhaps bliss about finally having a grasp on topics that have stressed me out all semester This is the perfect review for my finals next week, thank you so so much for your wonderfully impressive work!

[@pardonjoon8835]

omg! the made in abyss music in the background made me soooo happy! that's my favorite anime ever! thank you so much for everything, you're helping me pass my 18.06 exam tomorrow! you're the goat!

[@vedantgirnare9226]

Amazing set of videos man! I don't have words to describe it! This is what the internet is meant for.

[@RahulSharma-ht2xz]

totally love it, I learnt 10X time more after watching this video than reading my book 10 times.

[@abhishh_ek]

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.

[@usamasaddique7580]

Never seen such a detailed and great explanation of any topic. Excellent effort man. Keep teaching.

[@skyward-r3k]

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

[@alsthania826]

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!

[@tylervandermate]

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

[@firstkaransingh]

This is terrific.... Extremely well explained a concept as complex as SVD. Thanks a lot.

[@datboii8383]

i love your visualizations so much. they make understanding concepts we learn in uni a lot easier. like yes ik what im doing on paper, but why am i doing it? your videos make me understand that. looking forward to more content from u ! (and i’ll definitely be the on lookout for that video on principle component analysis 🙂)

[@danilocorreia5104]

These 4 videos enlightened me more than the past two weeks of machine learning class

[@RichJolly-e3z]

Beautiful. The comparison of the SVD to the Fourier Transform really cemented the ideas! Thanks.

[@sokkawatertribe2252]

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.

[@3xor3y]

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.

[@yashkokane4841]

Not everyday do I come across videos on youtube that blow my mind like this one did. Cannot thank you enough!

[@OuailOucherif]

This video is a piece of art , just like the fancy world of math and linear algebra , thanks for the efforts !

[@rolandocortez2405]

I can't wait for the principal component analysis video you promised 👀

[@ruiz_is_sleeping]

NAH WHAT HE EXPLAINED STUFF IN LIKE 12 MINS BETTER THAN MY LECTURER'S 1.5 HOURS i love you you're saving my linear alg finals

[@exoticcoder5365]

This video is gold, I have watched several videos about SVD, but this one explained the best

[@joarhussain6602]

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!

[@yehiamoustafa9801]

These 4 vedios are the best at explaining the matrices and the SVD , thanks a lot for your great effort

[@underfilho]

GREAT VIDEO!!! I'm studying this right now and we saw this as some way of change of basis in a way that the transformation be nicer, and also to do these things with approximation of images and to get the most important features of some data. It's great to have that way of geometric visualization too, and makes perfect sense with I have studied.

[@PFS-w5y]

Sir you are to be congratulated. I am always searching for an understanding of difficult mathematical concepts to be explained simply. You have done that in spades for this difficult concept of linear algebra. Your series of videos that lead up to your SVD explanation are pedagogical genius. Professor Gilbert Strang would be proud.

[@guywac]

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.

[@massimoc7494]

After being bogged down with math for a while a visualization proof helps understanding very much, thank you

[@RRRRRRRRRRRRRRR8964]

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!

[@Automan9]

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 🤤

[@westcoasthighway]

the visualization was very good and I just love the power and energy in your voice

[@formas1]

He thought no one would lotice My War playing as background music Huge thanks this is saving my day rn!

[@zilonghuang3377]

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.❤❤❤

[@sichangxu6209]

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!

[@ej8eid23i38]

The 4 videos and the Attack on Titan Ost during the visualization as the final part was perfect. Thank you sir

[@actualBIAS]

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.

[@karkaroff1617]

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.

[@Jonathan_man]

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.

[@mental4508]

Man, these videos are incredibly well made, good work. Also, I love the version of "My War" you played during the visualization :D

[@stanees9657]

You deserve to be remembered in my life.

[@panagiotisgiannikopoulos2147]

you gave me the final push to fully understand the SVD in depth. Just add I would propose a video to visualise matrices with imaginary numbers and conjugate transpose.. In any case was amazing thank you.

[@dennisalbert6115]

Lucky to finally find this page, been trying to understand matrices for randomization problem

[@Bolalexvalencia]

This should have way more views. Waiting for the next ones. Excellent!

[@kennybainbridge2473]

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. :)

[@anubhavdeep7016]

This is GOLD!!! Thakyou so much, looking forward to understanding NMF, QR Decomp etc.

[@MrSaimahesh]

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.

[@teaformulamaths]

I think the opposite about copying, I can praise innovation

[@winnieyang4843]

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!

[@prianshubhatia2759]

This four part series should be part of every linear algebra curriculum!

[@PRABHATHANUJAKOPPULA]

This video is a saviour.Thank you so much for such wonderful visualization. Please please please do more videos @visualkernel. Waiting for PCA

[@giaantran3810]

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.

[@DJSturm1]

Great job, looking forward for new videos- this is first video about SVD that actually clarified my understanding about it. Thank you!

[@AamirAliDrigh]

meanwhile Gilbert Strang took weeks to teach this. you have done it in 17 mins. unbelievable pedagogical skills man. keep up the good work.

[@吳宥瑄-c3j]

"a video in the future" 🥹🥹🥹 Please more videos!!!

[@officebatman9411]

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

[@asatorftw]

What a phantastic series. Truly appreciate your effort!

[@user-rg3or4kj3k]

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!

[@lyricass7810]

I just fuc**** love this channel, this video, and its creator...❤️‍🔥, thank you so much for the svd intuion Anna(in my language brother❤️). I just love all the maths community ❤️‍🔥.

[@rishabhgupta-he2wg]

Man, this interpretation is divine level stuff. You are so good! Please make more such videos

[@GeorgeWolfski]

I watched your 4 videos in a row. What a breathtaking journey! Are you still working on the video of principal component analysis? Highly looking forward to watching your another masterpiece!

[@mulezen9167]

This video is pure gold. More people should see it.

[@rockapedra1130]

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!

[@axolotl_observer]

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!

[@visualkernel]

Hope you had fun along the way !

[@erfanmirzaei705]

Briliant visualization and very nice interpretations. We are eagerly waiting for your thoughts and videos on connection between Fourier transform and SVD.

[@mamtfasc69]

This is an overwhelmingly good video mate, hats off

[@aldolunabueno2634]

A masterpiece! It was very helpful and now I feel like I know something huge. Thank you!

[@Teacute]

Super helpful, keep making more of these please 👌

[@HaritsElfahmi]

literally coming back here a few times just to rewatch this, awesome video

[@DiamondSane]

Finally, a both useful and beautiful, among just beautiful some2 videos.

[@nicorobin7666]

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

[@josiah9524]

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.

[@nenadilic9486]

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.

[@jiayichen1803]

What a clear and honest video! Can't wait to see the next ones

[@visualkernel]

Thanks bro !

[@Nikita_1912]

This video saved so much time, very well done! But i wasn´t expecting the crossover between Math and Aot.