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!
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 ?
@@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.
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.
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! 👏👏👏
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.
9:00 You have no idea how long I’ve been looking for a clear explanation of orthogonality and it’s practical application. I’ve now read 2 textbooks on la and am reading aa right now, and you are the only person to actaully answer WHY we want orthogonality besides linear independence. You just earned a sub
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!
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
Thank you so much for the video. It is really helpful to explain someone with this who do not have their background in linear algebra. Thanks again for all the effort. Its worth it.
imagine being so good that u can explain matrix composition using a chord in music 3:58. This explanation is itself multidimensional my brain is exploding
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!!
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!
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,
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
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.
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!
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
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
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!
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!
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!
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!!!
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!
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!
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.
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.
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;)
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.
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?
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
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.
@@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
@@omridrori3286 Well, this video is currently not advertised, and finding a video like this is pretty challenging. (I actually tried to TH-cam 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.
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!
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 ?
@@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.
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.
I feel like it's because most intro linear algebra courses only cover the more basic stuff that 3b1b had already covered.
hlw swagato sir, where are you from?? guessing you're A Bengali but from where??
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! 👏👏👏
thanks buddy !
I loved and appreciated 3B1B, but somehow, this here was more clearer.
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.
Soooo better visual math videos than anyone.... Just subbed bro.
Brilliant. I don't understand why the geometric interpretation is treated as if it doesn't exist in schools. Thank you a lot!
9:00 You have no idea how long I’ve been looking for a clear explanation of orthogonality and it’s practical application. I’ve now read 2 textbooks on la and am reading aa right now, and you are the only person to actaully answer WHY we want orthogonality besides linear independence. You just earned a sub
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!
The music note analogy is such a beautiful way to explain the decomposition of matrix transformations! Amazing video!
The best explanation I've seen in 25 years, counting from my first exposure to matrices as a freshman
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
This is literal gold, if you are reading this comment you hit a goldmine congratulations
Really hope you can make more videos ! The way you explain a concept is so elegant and makes it such a breeze to comprehend.
wow simply wow, I have not seen such a beautiful visualization.
This was so well made it got me kicking my legs in the air out of excitement especially at 9:22
Thank you so much for the video. It is really helpful to explain someone with this who do not have their background in linear algebra. Thanks again for all the effort. Its worth it.
imagine being so good that u can explain matrix composition using a chord in music 3:58. This explanation is itself multidimensional my brain is exploding
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!!
Check out the SVD one , even cooler
Amazing, you just explained a concept in 15 minutes that my teacher failed to explain in 4 lectures. Keep being awesome!
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!
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,
best teacher ever. I´ve never lernt a tough consept this fast + the background music is the most fitting thing.
This video is beautifully animated and straight to the point. Thank you for illustrating decomposition in such an elegant way.
The decomposition of a musical chord into the notes is such a beautiful touch !!! I am lucky I got to your channel.
Amazing to be honest. One of the rare channel to explain the intuitions rather than just the computations. Bravo !
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
extremely well done, keep this up because college students with bad linalg professors truly appreciate the content.
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.
Amazing, mind blowing explanation!!!! We need more tutors like you! I wish they taught like this in high school.
Brilliant! I wish professors emphasized this intuitive understanding more often
The logic flow renders much more understanding than other 'visual course', particularly about the eigenvector!!!
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!
THIS IS SICK! The best explanation I've ever seen on TH-cam
Absolutely beautiful brother
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
This is absolutely breath-taking!
WOW!!!
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
One of the best explanations in linear algebra I have ever seen. Subscribed. Keep up the good work.
Thank god you are making thsee video. Actually i just saw 3B1B eigen video but i understand here more accurately.
This explanation was phenomenal. Great job!
Insane visualisations!
Helped me in the understanding of diagonalisation of matrices immensely
Thanks a lot!!
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!
thank you sooo much for these videos. for some reason I remember/understand concepts so much easier when they have visual interpretations
It was nice to see the scalings and rotations done step-by-step, very helpful for a better understanding! ty
very helpful. thank you. never expect math can be so easy to understand.
One of the best tutorial videos I have ever seen. Thanks
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!
Visualization really helps with understanding. Thank you so much for the great videos
Watched this video again, and oh boy its so good!
Neo would be proud of these vids. Fantastic job!
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!
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!!!
This is absolutely awesome, surprised you don’t get as much recognition; really wonderful video
Great extension to 3b1b's Linear Algebra series, Thanks so much !!! it really help me build the intuition
love from India, 3blue1brown and you guys really made algebra beautiful; again.
thank you so much for introducing me to this. You've made my life easier through your work.
really loved this video!!!! thank you so much!!! made the concept so much clearer!
Very nice presentation. Like a great athlete, you make what you do seem effortless.
these videos are amazing，Thank you for sharing this with us.
Thank you so much for this video it really helped me better understand the concept!
The guitar chord analogy was a nice touch
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!
Thank you for this video. Thank you very much. It's awesome. I want more of your videos.
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!
It was literally perfect. Thank you!
Really great vid!! So glad I was discovered this channel!!
This video was infinitely awesome!
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.
A pretty much under-appreciated course on LA
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.
Most clear and illuminating
So good!!!! Especially your explanation of eigen stuff.
Amazing videos. So underrated!!
Amazing. I am stunned. Thank you.
Very clear transparent video. It has also powerful mesmerizing effect. Calming satisfying Yoga-effect😅
These are great videos. Please make more!!!
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;)
This is an amazing production. Thanks
What an awesome explanation!
3b1b should shout this out man. Legend
Please keep doing this masterpieces! Thank you!
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.
This is amazing, thank you for all your high quality videos! Can't believe this has comparatively few views
Fantastic work, thank you for this
Why did you stop making videos, bro? This is GOLD!!
This was insane. Thank You so much!
So happy to stumble on these, you got a new subscriber today!
you are a genius!!! wish you were my math teacher
Yo this vid might of just saved for my finals thx düd
Excellent video! Would love to see more content like this :)
really supreme video! thanks a lot!
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?
Amazing explanation. Keep up this good work
This actually complements some of the illustrations 3B1B didn't demonstrate.
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
Thank you very much!!! Hope you will find the time to make more video's:) You helped me a lot!:)
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.
@@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
@@omridrori3286 Well, this video is currently not advertised, and finding a video like this is pretty challenging. (I actually tried to TH-cam 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.
@@visualkernel
When i really wait for that every day i check please i really want to know svd
Video is transformative
love this videos...they´re so helpful......thanks man.....keep doing it......by the way, the chords detail was pretty nice....
Thank you so much for your help!!!
Keep up great work man, I hope you can release more😢
I LOVE THIS VIDEO