Linear Algebra: Singular Value Decomposition (Full lecture)

[Spacexioms]

This is the greatest video I’ve seen on svd

[BharathSaiS]

The first time you see a math teacher with a smile..

[masakmemasak]

the best lecture for SVD right now for me! as you mention every step clearly in detail and flow..it really help me who is not into this topic during my bachelor.. thank you Dr! :D

[amirhosseindaraie]

Dear Dr. Hower, you are an amazing teacher. I enjoy watching your lectures.

[redouaneabegar]

Best numerical application of SVD I've ever found on YouTube. Thank you ma'am

[davidpabon]

Great lecture on SVD, thank you so much doctor Hower

[spencerfradkin]

Dr. Hower,

My name is Spencer and I was a student in your Calc 2 class at FAU a couple Summers ago. Your calc 2 class was my favorite class in undergrad. I was searching youtube for svd videos for a graduate class I'm taking and I can't believe I came across your channel. This video is exactly what I needed and it's explained as well as your calc 2 lectures. Thanks!!!

[menugrg]

The best explanation of Singular Value Decomposition.. many thanks Dr. Hower.

[bashiruddin]

The sort of lecture we wish we could have found at the start of semester.Thanks a lot

[electrocrats]

nice explanation mam, Respect from INDIA

[moin]

Keep up the energy! Thank you for this video.

[mihirp]

Cool and awesome teaching ma'am👍Thank you very much

[samueldarenskiy]

Can you please explain why the sigma diagonals must be squared?

[rafaeljabbour]

At 39:00 you used ker(row(V)) to find the third unit vector, is it always the case that you can use that? or do you sometimes need to use Gram-Schmidt process?

[ungarlinski]

@21:00 So if I wanted my Sigma matrix to have the columns switched so that is was not not diagonal anymore so that the sigma1 and sigma2 values were on the off diagonal, I could just use this same procedure and solve for the new U? I know this would no longer be SVD, but I'm curious about this kind of decomposition too.

[climitod]

31:50 I am very confused how you got v here. I did the ker(A^(T)a -9I) = {<1, 0>, <0, 0>) and I did it for 81. I got the same vectors as you but you associated them differently I did the identity matrix for v because that's the order that makes sense and how its defined in the text with v1*k1 for k=eigenvalues.

[russellsharpe]

Thank-you for this clear exposition. However, I thought you were going to prove that every matrix has such a decomposition. But at 12:45 you simply assume it does, and then derive facts about sigma and V based on this assumption. That is not sufficient to show that such a decomposition exists, is it?