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

Жыл бұрын

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

Жыл бұрын

@@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

Жыл бұрын

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

Жыл бұрын

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

@vnitian2233

Жыл бұрын

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! 👏👏👏

@visualkernel

Жыл бұрын

thanks buddy !

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!

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

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

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

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

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

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,

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

This explanation was phenomenal. Great job!

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

Жыл бұрын

Check out the SVD one , even cooler

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

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

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

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

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

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!

Amazing. I am stunned. Thank you.

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

This video was infinitely awesome!

Please keep doing this masterpieces! Thank you!

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

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

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

This is an amazing production. Thanks

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

Fantastic work, thank you for this

Amazing videos. So underrated!!

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

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!!!

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

Thank you so much for your help!!!

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

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

really supreme video! thanks a lot!

Most clear and illuminating

Amazing explanation. Keep up this good work

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

Neo would be proud of these vids. Fantastic job!

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

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

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

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

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!

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.

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

this is fantastic!

Brilliant! I wish professors emphasized this intuitive understanding more often

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 this video it really helped me better understand the concept!

Beautiful!

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

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!

Thank you so much.

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

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

Brilliant! 👏👏👏

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

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

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

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!

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

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

brilliant!!

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.

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;)

Video is transformative

Very nice, thank you very much:)

Thank you so much sir :)

Brilliant!

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

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

Respect for you

Great video

The guitar chord analogy was a nice touch

sublime

A pretty much under-appreciated course on LA

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

Excellent

3b1b should shout this out man. Legend

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

@visualkernel

2 жыл бұрын

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

2 жыл бұрын

@@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

2 жыл бұрын

@@omridrori3286 Well, this video is currently not advertised, and finding a video like this is pretty challenging. (I actually tried to KZread 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

2 жыл бұрын

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

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

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?

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

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

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.

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

Thanks

Fantasic

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

@visualkernel

9 ай бұрын

Is this the Legendary Vinam Arora himself ?

@vinamarora7049

9 ай бұрын

@@visualkernel Ye buddy absolutely loved the video!

Nice video mate just wanted to know how did you get the conceptual knowledge

Great

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.

@stayinthepursuit8427

Жыл бұрын

yes . Eigenvalues scale. Eigenvectors rotate.

also wouldnt the eigen basis rotate the standard plane onto its transformation?

Thx for the video! Couple of questions: 1. Does the SD(spectral decomposition) method, work only for full rank symmetric matrices? What are in general the conditions for the SD to work? 2. Would this work also for complex-valued symmetric matrices?

@Lonewolf-xv1bl

5 ай бұрын

2. Yes. Complex valued symmetric matrix is called Hermitian matrix. You can perform similarity transformation with the help unitary matrix. Which are complex analogue of orthogonal matrix. Symmetric matrix S => Hermitian matrix H Orthogonal matrix O => Unitary matrix U You have O'SO similar for complex case You get (U*)'HU Here * represents complex conjugation and ' represents trasponse. There is single notation to represent it called dagger. It is not available in my keyboard so I broke it down. You have to take complex conjugation and then transport it.

2:46 Q^T = Q^(-1) this is only true if Q is Orthonormal, but for the second and the third column of Q from the left, their magnitude exceed 1, I don't see how this still holds. Can you explain?