Visualize Spectral Decomposition | SEE Matrix, Chapter 2

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  • Опубликовано: 30 окт 2024

Комментарии • 200

  • @swagatochatterjee7104
    @swagatochatterjee7104 2 года назад +251

    I literally have zero ideas, why does this series have so less views. This is literally the best extension to 3b1b's Linear Algebra series. This is exceptionally exquisite! Subbed!

    • @visualkernel
      @visualkernel  2 года назад +43

      EoP (Essence of Linear Algebra) is exactly what inspired this series. I never want to compare anything I make to the legendary 3b1b, but your comment were spot on, I hope this series can somewhat be an informal extension of of EoP. Just like in most college course linear algebra course, the first half focus on things like (vector, range, null space, determinants, linear dependence); the second half of course is almost exclusively focusing on matrix decomposition, and personally I thought the visual interpretation of them were equally valuable hence this series. Appreciate your very encouraging words, did you check out SVD by the way ?

    • @swagatochatterjee7104
      @swagatochatterjee7104 2 года назад +4

      @@visualkernel yes. It was exactly what I needed to know. I always wanted to know why all of a sudden doing the eigen decomposition of AA^T was thought of to calculate the SVD. Now I understand.

    • @ssssssstssssssss
      @ssssssstssssssss 2 года назад +2

      He needs to put out more videos. Viewers will come but not with just four videos. He’s got to consistently put them out.. I think he has a ton of potential.

    • @LexiZ0708
      @LexiZ0708 Год назад +1

      I feel like it's because most intro linear algebra courses only cover the more basic stuff that 3b1b had already covered.

    • @vnitian2233
      @vnitian2233 Год назад +1

      hlw swagato sir, where are you from?? guessing you're A Bengali but from where??

  • @hansenmarc
    @hansenmarc 2 года назад +102

    I think 3B1B would be proud. This provides very nice intuition into how to think about spectral decomposition and the role of symmetric and orthogonal matrices in it. Well done, sir! 👏👏👏

    • @visualkernel
      @visualkernel  2 года назад +7

      thanks buddy !

    • @NaaneVinu
      @NaaneVinu Месяц назад +1

      I loved and appreciated 3B1B, but somehow, this here was more clearer.

  • @supdawg7811
    @supdawg7811 4 месяца назад +7

    My god, no one in the math community intuitively spoon feeds me this stuff, but that's what I need. And these videos do exactly that. This is fantastic. I truly believe that the people that substantially innovate in any field are the ones that understand that actual intuition.

  • @darshan5044
    @darshan5044 Год назад +15

    Brilliant. I don't understand why the geometric interpretation is treated as if it doesn't exist in schools. Thank you a lot!

  • @leticiabarbaneramenezes2751
    @leticiabarbaneramenezes2751 11 месяцев назад +5

    this series has just become the best videos I've EVER watched in my life! Never thought I'd cry in the middle of my Uni's library bc i got emotional on how spectacular and genuinely beautiful linear algebra is!

  • @Colby_ye
    @Colby_ye 10 месяцев назад +3

    The music note analogy is such a beautiful way to explain the decomposition of matrix transformations! Amazing video!

  • @Automan9
    @Automan9 11 месяцев назад +3

    God fucking damn bro. Even my two brain wrinkles managed to understand the intuition behind decomposition. The most elegant explanation I've ever seen of the subject, and the lead up to it with all the topics was masterful

  • @JunZhang-ralphjzhang
    @JunZhang-ralphjzhang Год назад +3

    The best explanation I've seen in 25 years, counting from my first exposure to matrices as a freshman

  • @willwu7353
    @willwu7353 2 года назад +7

    Damn this is so intuitive! Its easy to get lost in matrix multiplication but this was a superb reminder for me to just step back and just think of them as geometric transformations. Its actually kind of earth shattering. TY!!

    • @visualkernel
      @visualkernel  2 года назад +1

      Check out the SVD one , even cooler

  • @max8110
    @max8110 9 месяцев назад +2

    This may not mean much from a stranger on the internet, but I don't know if I can convey with words how amazing and effective this video is. This is a masterpiece, and it stands far above the numerous math content I've seen (believe me, I've seen a lot). You have a real and rare skill for being extraordinarily concise and intuitive. Keep it up,

  • @lakshyadugar1522
    @lakshyadugar1522 6 месяцев назад +5

    Probably the best video I've come across explaining this. This not only made SVD crystal clear but also cleared so many other concepts within Linear Algebra not even directly related to SVD. So glad to have come across this. Looks like you haven't uploaded in a couple of years, hoping for new videos!

  • @nguyenquannnn8942
    @nguyenquannnn8942 10 месяцев назад +3

    Amazing, you just explained a concept in 15 minutes that my teacher failed to explain in 4 lectures. Keep being awesome!

  • @aryanpinto238
    @aryanpinto238 2 месяца назад +1

    best teacher ever. I´ve never lernt a tough consept this fast + the background music is the most fitting thing.

  • @dimitrismylonas4159
    @dimitrismylonas4159 Год назад +10

    This video is beautifully animated and straight to the point. Thank you for illustrating decomposition in such an elegant way.

  • @md.salahuddinparvez6578
    @md.salahuddinparvez6578 Год назад +1

    The decomposition of a musical chord into the notes is such a beautiful touch !!! I am lucky I got to your channel.

  • @nicolasmanelli7393
    @nicolasmanelli7393 3 месяца назад

    Amazing to be honest. One of the rare channel to explain the intuitions rather than just the computations. Bravo !

  • @rushirajparmar9602
    @rushirajparmar9602 Год назад +2

    Amazing, mind blowing explanation!!!! We need more tutors like you! I wish they taught like this in high school.

  • @kaansun8601
    @kaansun8601 7 месяцев назад +1

    This is literal gold, if you are reading this comment you hit a goldmine congratulations

  • @yuhaiwu-z7y
    @yuhaiwu-z7y 11 месяцев назад

    The logic flow renders much more understanding than other 'visual course', particularly about the eigenvector!!!

  • @Scaryder92
    @Scaryder92 Год назад +1

    Thank you, this was beautiful and very informative! In my opnion, getting the intuition behind a concept is the best way to remember it and to apply it in a different context

  • @karlrombauts4909
    @karlrombauts4909 2 года назад +8

    It took some digging, but I am so glad that I found your videos. These are absolutely fantastic! I really hope that you get more subscribers and that you continue producing content. These videos have been exactly what I needed. Amazing work!

  • @coletivismo4635
    @coletivismo4635 11 месяцев назад

    Brilliant! I wish professors emphasized this intuitive understanding more often

  • @gustavopaiva4676
    @gustavopaiva4676 Год назад +1

    Really good video man, I was doing the exercises like a robot just applying steps in a specie of algorithm without knowing really the meaning of it. Now I can visualize this transformations and this decompositions in my head, thank you so much

  • @LydellAaron
    @LydellAaron 3 месяца назад

    Very well done! You've done a very good job and now (meaning I've been around and around, many videos on this topic and advance mathematics) I would recommend people watch yours first because you lay out all the ideas and connect them, and the visual geometries behind them.

  • @epistemophilicmetalhead9454
    @epistemophilicmetalhead9454 Месяц назад +1

    This was so well made it got me kicking my legs in the air out of excitement especially at 9:22

  • @rohithsudarshan6524
    @rohithsudarshan6524 Год назад

    extremely well done, keep this up because college students with bad linalg professors truly appreciate the content.

  • @hjop010
    @hjop010 Год назад +1

    One of the best explanations in linear algebra I have ever seen. Subscribed. Keep up the good work.

  • @davidsousa511
    @davidsousa511 Год назад +1

    I find this impressive, this concepts are really hard to understand but the order and the way they are explained made very much sense to me! Thank you!

  • @the.potential.dropout
    @the.potential.dropout Месяц назад +1

    Absolutely beautiful brother

  • @meet13321
    @meet13321 Год назад +5

    Thanks for these kind of content, I feel by having these kind of content you are helping people to understand power of mathematics and help apply these concepts which otherwise need tedious study of mathematical formulas , which helps people like us to bridge the gap to understand other applied solutions from these basics. Keep it up , world is converging and future solutions can only be solved when more people understand the basics intuitively and apply to solve new problems of world

  • @AnaPaladi
    @AnaPaladi Год назад

    It was nice to see the scalings and rotations done step-by-step, very helpful for a better understanding! ty

  • @kakunmaor
    @kakunmaor Год назад

    THIS IS SICK! The best explanation I've ever seen on RUclips

  • @charleskolozsvary8714
    @charleskolozsvary8714 2 года назад +4

    This is absolutely awesome, surprised you don’t get as much recognition; really wonderful video

  • @Stefabro
    @Stefabro Год назад

    thank you sooo much for these videos. for some reason I remember/understand concepts so much easier when they have visual interpretations

  • @neilchen2570
    @neilchen2570 2 года назад

    This is such an underrated video about the topic about matrix decomposition! I really like the approach that helps me visualize the meaning of the topic tremendously! Keep up the hard work!!!

  • @Baaarain
    @Baaarain Год назад

    One of the best tutorial videos I have ever seen. Thanks

  • @arz3nal
    @arz3nal Год назад

    This is great! I took a course in Operator Theory and for the life of me couldn't visualize the spectral theorem in any intuitive way. I wish I found this video months ago!

  • @yudzu8820
    @yudzu8820 7 месяцев назад

    excellent videos. I am so glad, that I found it. Thank you for a lot of work that you've done to make these excellent visualizations. Also the structure is intuitive and logically ordered. Bravo!

  • @marazak6390
    @marazak6390 9 месяцев назад

    Insane visualisations!
    Helped me in the understanding of diagonalisation of matrices immensely
    Thanks a lot!!

  • @moritzh409
    @moritzh409 2 года назад +2

    Dude I think this might be my first comment on youtube, but you deserve it haha. This series got me understanding matrices at a level even deeper than youtube-linalg's godfather 3blue1brown:) You ROCK! and dope logo you got for your channel! keep it up, I'll be there;)

  • @ahmedsobhy8792
    @ahmedsobhy8792 Год назад

    Visualization really helps with understanding. Thank you so much for the great videos

  • @jphicks1984
    @jphicks1984 Год назад +1

    Brilliant videos that really add to the understanding and intuition of these concepts. As others have said these videos deserve far higher views, and hopefully one day you will find time to make more!

  • @asatorftw
    @asatorftw 6 месяцев назад +1

    This explanation was phenomenal. Great job!

  • @gohilramdevrajeshbhai5254
    @gohilramdevrajeshbhai5254 Год назад

    Wow! This whole series is so beautiful! First time I understood so many important things!
    Thanks a ton Sir. Lot of gratitude towards you for this way of knowledge!

  • @mychen5520
    @mychen5520 Год назад

    Great extension to 3b1b's Linear Algebra series, Thanks so much !!! it really help me build the intuition

  • @ryan_chew97
    @ryan_chew97 Год назад

    Holy crap, the Manim animations are incredible. I want to use Manim for my own channel for unrelated to math topics, and I am going to take inspiration from your style. It's probably the best I've seen aside from 3B1b.

  • @kevinbyrne4538
    @kevinbyrne4538 7 месяцев назад

    Very nice presentation. Like a great athlete, you make what you do seem effortless.

  • @nitika9769
    @nitika9769 9 месяцев назад

    thank you so much for introducing me to this. You've made my life easier through your work.

  • @xavaraexe
    @xavaraexe 3 месяца назад

    Ohh god, why did this guy stopped uploading videos??? Its been 2 years. Why didnt you continue?? Your explanation were very smooth, even a 3rd grader can understand this.

  • @YuanpuLi
    @YuanpuLi Год назад

    very helpful. thank you. never expect math can be so easy to understand.

  • @fnegnilr10
    @fnegnilr10 Год назад

    Neo would be proud of these vids. Fantastic job!

  • @nikhilnawaghade3697
    @nikhilnawaghade3697 2 месяца назад

    Thank god you are making thsee video. Actually i just saw 3B1B eigen video but i understand here more accurately.

  • @TMK264
    @TMK264 3 месяца назад

    This is absolutely breath-taking!
    WOW!!!

  • @jeremykusnadi5148
    @jeremykusnadi5148 3 месяца назад

    Why did you stop making videos, bro? This is GOLD!!

  • @srikanthraghavan2092
    @srikanthraghavan2092 2 года назад +1

    Really great vid!! So glad I was discovered this channel!!

  • @advitranawade3039
    @advitranawade3039 2 месяца назад

    Incredible video. Just one point to note: Q was mentioned to be a matrix that 'rotates' the standard basis to the eigenvector basis. Actually, it's the other way round. It takes vectors denoted in the eigenvector basis and denotes them in the standard basis... For example, given the vector [1, 0] in the eigenvector basis: it represents one unit along eigenvector e1 and 0 units along eigenvector e2, or in standard terms, it represents e1. Given to this matrix, it indeed 'spits out' e1 - the same vector but now in the standard basis. This was actually a big point of confusion for me in uni so just thought to clarify it.

  • @CamEron-nj5qy
    @CamEron-nj5qy Год назад

    The guitar chord analogy was a nice touch

  • @karennn3973
    @karennn3973 Год назад +1

    really loved this video!!!! thank you so much!!! made the concept so much clearer!

  • @asatorftw
    @asatorftw 6 месяцев назад

    Watched this video again, and oh boy its so good!

  • @Es4la
    @Es4la Год назад

    This is amazing, thank you for all your high quality videos! Can't believe this has comparatively few views

  • @jim8730
    @jim8730 Год назад

    So good!!!! Especially your explanation of eigen stuff.

  • @arkaroy8172
    @arkaroy8172 5 месяцев назад

    love from India, 3blue1brown and you guys really made algebra beautiful; again.

  • @MaxxTosh
    @MaxxTosh Год назад

    So happy to stumble on these, you got a new subscriber today!

  • @adaslesniak
    @adaslesniak 8 месяцев назад

    Thank you for this video. Thank you very much. It's awesome. I want more of your videos.

  • @ozachar
    @ozachar Год назад

    Most clear and illuminating

  • @Alpasonic
    @Alpasonic Год назад

    Very clear transparent video. It has also powerful mesmerizing effect. Calming satisfying Yoga-effect😅

  • @Vjdkgaming
    @Vjdkgaming 9 месяцев назад

    Thank you so much for this video it really helped me better understand the concept!

  • @jamespeck1827
    @jamespeck1827 Год назад +1

    Excellent video! Would love to see more content like this :)

  • @cardinalblues7121
    @cardinalblues7121 Год назад

    these videos are amazing,Thank you for sharing this with us.

  • @zenicv
    @zenicv Год назад

    A pretty much under-appreciated course on LA

  • @ManeeshaShivanand
    @ManeeshaShivanand Месяц назад

    These are great videos. Please make more!!!

  • @simonekockelkorn1235
    @simonekockelkorn1235 2 года назад +2

    Thank you very much!!! Hope you will find the time to make more video's:) You helped me a lot!:)

    • @visualkernel
      @visualkernel  2 года назад

      It is interesting how I make this kind of video while expecting to be seen by no one. But youtube recommendation algorithm just does interesting things, leading people to the edge of the internet. And I am very glad if it could have offered an alternative perspective on how we view matrix decomposition. SVD coming out soon, that will be a good one.

    • @omridrori3286
      @omridrori3286 2 года назад

      @@visualkernel
      Why expecting to see by no one ? I personally really like math videos and these are really great and definitely give good fight for 3blue1brown

    • @visualkernel
      @visualkernel  2 года назад

      @@omridrori3286 Well, this video is currently not advertised, and finding a video like this is pretty challenging. (I actually tried to RUclips search "Visualize Spectral Decomposition" explicitly, and my video does not even come out ). So I think it's very interesting how you landed on this piece of recommendation. And about 3b1b ... I think everyone who makes math video can only asymptotically approach the half of what he is. Thank you Omri, for your words of encouragement.

    • @omridrori3286
      @omridrori3286 2 года назад

      @@visualkernel
      When i really wait for that every day i check please i really want to know svd

  • @amkhrjee
    @amkhrjee 10 месяцев назад

    This video was infinitely awesome!

  • @soroushsobhkhiz9383
    @soroushsobhkhiz9383 Год назад

    Amazing videos. So underrated!!

  • @user-wr4yl7tx3w
    @user-wr4yl7tx3w 8 месяцев назад

    This is an amazing production. Thanks

  • @ChillyFries444
    @ChillyFries444 Год назад

    3b1b should shout this out man. Legend

  • @debangonachakraborty2502
    @debangonachakraborty2502 3 месяца назад

    What an awesome explanation!

  • @klaotische5701
    @klaotische5701 Год назад

    This actually complements some of the illustrations 3B1B didn't demonstrate.

  • @canbagrgan8731
    @canbagrgan8731 4 месяца назад

    It was literally perfect. Thank you!

  • @nenadilic9486
    @nenadilic9486 Год назад

    Amazing. I am stunned. Thank you.

  • @andywang4189
    @andywang4189 11 месяцев назад

    Keep up great work man, I hope you can release more😢

  • @MrWater2
    @MrWater2 Год назад

    Please keep doing this masterpieces! Thank you!

  • @franciscorosetavazmonteiro1227

    Yo this vid might of just saved for my finals thx düd

  • @ivarholmlund4962
    @ivarholmlund4962 10 месяцев назад

    Beautiful video, i was amazed about the quality and how good the explanations and vizualisations were!
    I dont see the chapter 1 part anywhere, is there only supposed to be the chapter 2?

  • @kevinj7192
    @kevinj7192 Год назад

    I love these videos! I've watched 3Blue1Brown linear algebra videos. They are good but more conceptual math. These videos show how to implement linear algebra to computer graphics. I'm lucky to find it when I search svg

  • @marcelolarrea4583
    @marcelolarrea4583 Год назад

    love this videos...they´re so helpful......thanks man.....keep doing it......by the way, the chords detail was pretty nice....

  • @danielschreck9083
    @danielschreck9083 Год назад +1

    Amazing video, fantastic job. Small mistake - at 14:50, the labels for Q and L are incorrectly swapped - L is labeled as the eigenvector matrix and Q is labeled as the eigenvalue matrix, but the reverse is correct.

  • @the_batman6506
    @the_batman6506 4 месяца назад

    you are a genius!!! wish you were my math teacher

  • @VinayakKannan-s5f
    @VinayakKannan-s5f 10 месяцев назад

    Fantastic work, thank you for this

  • @TheKrasTel
    @TheKrasTel 2 года назад

    Bro just keep making these vidoes and the views will eventually come, it is literally inevitable!

  • @yasseralg3928
    @yasseralg3928 Год назад

    Amazing explanation. Keep up this good work

  • @Joy_Full1333
    @Joy_Full1333 5 месяцев назад

    Im feeling kinda sad because i can only found these amazing visually explained videos when i have project at uni.

  • @galiyabanu
    @galiyabanu 8 месяцев назад

    really supreme video! thanks a lot!

  • @visheshgoyal5903
    @visheshgoyal5903 Год назад

    Video is transformative

  • @billylee5624
    @billylee5624 6 месяцев назад

    This has gotten me to see the linear transformations of these "sandwich" estimators. I wonder how we can visualize econometric estimators like the basic OLS (X'X)^-1X'Y and it's covariance matrix (X'X)^-1(X'e')(eX)(X'X)^-1 and even longer matrix multiplication models.

  • @ruti_1494
    @ruti_1494 Год назад

    Thank you so much for your help!!!

  • @Ocara31
    @Ocara31 6 месяцев назад

    Please, continue this series. Make about PCA !!!

    • @wei-k7u
      @wei-k7u 3 месяца назад

      我也是因为PCA来看hhh

  • @mEm__96
    @mEm__96 Год назад

    I now understand why many people do not like math. Because they didn't see videos like these.

  • @FathahiMuthedath
    @FathahiMuthedath 4 месяца назад

    Great content

  • @vinamarora7049
    @vinamarora7049 Год назад

    Around 4:00, the parallels between decomposing a matrix into simpler operations and decomposing a chord into its notes.. 🤯

    • @visualkernel
      @visualkernel  Год назад

      Is this the Legendary Vinam Arora himself ?

    • @vinamarora7049
      @vinamarora7049 Год назад

      @@visualkernel Ye buddy absolutely loved the video!