What is the Singular Value Decomposition?

A visualization of the singular value decomposition and its properties.

Music:
All music by Benjamin Tissot

[pablorc]

Thank you, I think I now understand the bigger picture of what SVD actually is, beyond just the formula. You remind me very much of 3B1B.

[saketdeshmukh]

after watching gilbert strang I needed exactly this to visualize and understand very clearly. You taught most difficult to explain concept in Linear algebra, Machine learning and even deep learning in 7 minutes. Really grateful. You are at the level of 3blueandbrown and gilbert stang in terms of explaining difficult concept like its understandable to even beginners. Keep the good work. I would subcribe for paid contents for sure. Sadly very under appreciated channel but hope people will make it popular. Waiting for PCA.

[stefanandritoiu]

If anyone is confused at 2:55, why he is multiplying by V transpose and not the inverse, to get rid of V on the left side. It's because V is orthogonal matrix (that is how we defined it to be), and the transpose of an orthogonal matrix is equal to its inverse. This stems from the fact that if a matrix Q is orthogonal then QQ_T = Q_TQ = I

[schwaartz]

Make the sequel god damn it. I've been waiting for 3 years.

[adityakhedekar]

you explained it better than gilbert strang

[iagodantasf]

Bro, please make this second video relating to PCA, I beg you. Your explanations are the best

[vidajohn]

Great video, thank you. Eagerly waiting for your next PCA video.

[mysanoop]

At 2:55, inverse(V) is equal to transpose(V) because V is an orthogonal matrix

[erwanquintin]

I only have one word in reaction to your video: wow

This so well done man

[gmcgfml]

Where is the next video about PCA, loved this video.

[emersonruizrico]

Great video! Digestible and beautifully animated. This channel can become a good complement to 3b1b.

[omridrori]

Wowww when the next part ?!
It’s amaizing

[dawne]

This is the clearest explanation I've been able to find thank you!!

[momidimidhilesh]

I was looking for SVD in 3blue1brown channel. And you created using same library. Thank you

[kaustuvray]

Thanks so much.
This is a whole new perspective for me.
Loved it!!!!
Keep up the amazing work

Manim will help in creating a lot of amazing content.

[debashishdutta]

Eagerly waiting for your next video on PCA. Please upload soon. This video was brilliant.🤩💥💥

[arminneashrafi]

Hi! I was wondering when you would upload the PCA video, your method of explanation was really lucid and enlightening!

[marlondeoliveiragomes]

Great work, keep it up!

Minor typos at 3:45 (eigendecomposition), 5:21 (maximum).

[MohammedQaiss-egis]

one of the best videos I have ever seen. keep up the good work

[josephj]

A video that really helps!!! Thanks, buddy please continue to make videos!

Love from India!