Thank you Dr. Strang, TAs, and MIT for allowing me to pursue my dreams.

Ben Harris! You are awesome. Thanks Professor Strang for choosing this awesome team of TAs. They have all done an extraordinary job. I have become fan of all of them.

Hey Ben, this is an amazing video, thank you so much! This really helps me to understand the lecture.

Ben. You're amazing! I love your recitation videos. Awesome jobs!

I didn't like the numbers in C^TC so I took CC^T searching for U to see if I got better numbers and I did. its a matrix with first row vector being (50,30) and second row vector being (30,50). Just in case someone else also didn't want to calculate 26*74-18^2

Correct U is : 1 / sqrt(2) * [-1 1] [ 1 1]

Thanks, that's really helpful.

This video is gonna save my test tomorrow thank you

Thank you Ben!

The final answer for U has a typo, the (1,1) entry should have a -ve sign, not the (2,1) entry.

@davidhcefx

5 жыл бұрын

Mark Worrall I think you’re right

@archidar1

4 жыл бұрын

No, the answer shown in the video is correct. I verified by hand and using Matlab.

@confusionreigned

3 жыл бұрын

U*U has to equal the identity matrix. It's easy to see this doesn't work with U as is written in the video without correcting the typo.

@mailoisback

3 жыл бұрын

@@confusionreigned not U*U but U*U^T, and it actually works with the correct and the wrong U, you can check that U*U^T = I in both cases.

@confusionreigned

3 жыл бұрын

@@mailoisback yeah sorry I meant U*U^T. But unless you fix the typo, you don't get back to C = UEV^T as desired.

Hey Ben! Awesome job!

Much Help.Thx

why did he change the sign of elements of U at last

at the end. how he made the unit length. kzread.info/dash/bejne/ooeWw8ixdKvKl6g.html

@cupofcompsci3228

4 жыл бұрын

He divided the value in each column by the corresponding values of the sigma matrix ((20)^(.5) and 80^(.5) respectively)

@justpaulo

3 жыл бұрын

He divides the vectors by their length : || -√10 √10 || = √(10+10) = √20 = 2√5 || 2√10 2√10 || = √(4*10 + 4*10) = √80 = 4√5 It turns out that those values (2√5 and 4√5) are also the values in ∑ so you can read U directly.

My exam asked to SVD a 4x4 matrix by hand where all the numbers in the matrix were greater than 10. I skipped it!

Short videos are so much better.

Why for sigma square root is taken???

@adammehdi4934

2 жыл бұрын

The eigenvalue matrix of (A.transpose)(A) is SIGMA^2. After that, we want to use the equation AV = U(SIGMA), so we have to take the root. And for sqrt(SIGMA^2), we just take the root of each element. Hope that helps.

i took a different eigen vector and now my answer is all wrong and i made the same mistake professor strang made...... im so confused...

@sedahmo5601

4 жыл бұрын

Dr. Strang fixed his mistake in later video (I think it's sometime in L 32). Nevertheless he explained the choice in a much clearer way in the new series 18.065S (Lecture 6, around 20:20). The point of SVD is to find a series of vs satisfies Sv = sigma·u (thus the matrix). So v and the (semi)-positive singular value, sigma, should be chosen first, and then u. u could be calculated by Av/sigma. And it is easy to verify that the result us are also orthonormal eigenvectors. The deep reason why u and v can't be chosen arbitrarily like Q in symmetric matrix (S= QAQ^T) is that the middle matrix sigma is not a set fo "eigenvalues"( i.e. singular values) that satisfy the properties in symmetric case.

@madhatfox1

4 жыл бұрын

@@sedahmo5601 Where can I find the 18.065S series ?

@Ashutoshlakra

3 жыл бұрын

@@madhatfox1 kzread.info/dash/bejne/pI2umpWRgNvPitI.html