SVD Visualized, Singular Value Decomposition explained | SEE Matrix , Chapter 3 #SoME2

A video explains Singular Value Decomposition, and visualize the linear transformation in action.

Chapters:
0:00 SVD Intro
1:17 Visualize a Rectangular Matrix ?
5:16 Creating Symmetric Matrix
7:17 Singular Vectors and Singular Values
8:55 SVD Formula Dissection
10:05 The Visualization
12:54 Is this SVD ?
15:16 The Next Journey

Video Sins:

This video wouldn’t be possible without the inspiration of the legendary 3b1b :

and the animation software - Manim, which he wrote:

and the Manim Community:

Music Credit:
2. "First Layer" ost from an anime called Made In Abyss

[bananalord]

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

[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

[sumansan]

People like you will have a special place in heaven ❤

[molackanil]

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.

[marcelogranja]

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

[joarhussain]

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!

[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!

[johnstuder]

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 YouTube 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?

[JimmyMGhill]

It's hard to pay attention when you recognize all the anime songs😂 good job either on SVD and sounds!

[sichangxu]

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!

[preetysingh]

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..!!🙂🙏

[rolandocortez]

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

[MrRykooo]

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.

[markclintworth]

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!!

[saleemun]

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.

[francoisvictor]

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.

[dmitryr]

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:)

[vedantgirnare]

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

[basedland]

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

[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.