Singular Value Decomposition (the SVD)

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

The SVD factors each matrix into an orthogonal matrix times a diagonal matrix (the singular value) times another orthogonal matrix: rotation times stretch times rotation.

License: Creative Commons BY-NC-SA

[Sky-pgxy]

I can’t express how amazing this video is. I have taught from a number of textbooks in different undergrad linear algebra classes, and I’ve never in my life seen an explanation of SVD as good as this one.

[chrisjiang]

I used to watch Prof. Strang's videos when I was a first year undergrad. Never thought I would revisit this during my master as I am learning about PCA... Time flies yet Prof. Strang is forever

[handongfeng]

No any other guys can teach algebra better than this Professor. He is the teacher's teacher, the best of the best. Respect!

[qantum]

With all due respect, on which basis people did thumbs down this outstanding piece of algebra. If I had Profs. like Sir Gibert Strang at my early university years, I would've reached far beyond my own expectations. Your teaching is outstandingly straightforward Sir.

[babaumar]

The best linear algebra by all standards. He makes it look so simple. This explanation of SVD and PCA blew my mind. I salute you prof.

[jennariseley]

I have been trying to understand PCA all semester. I didn't realise that I would finally 'get' it after watching this video on SVD. Thank you so much Dr Strang and MIT!

[mtp]

Gilbert Strang is a genius on making difficult linear algebra topics understandable. I really appreciate his great work on being a powerful teacher.

[VenkataRamaRajuLolabhattu]

eigen people (or person) is the one of the greatest examples by Proff. Gilbert Strang. This one statement cleared many questions about PCA. Can't thank him enough, great professor. Thank you

[Hnek]

3:35 "And what do I have? Well, I've got six matrices..." LOL

[shivamkak]

I have watched this several time over the course of the last year, and each time I have gained a deeper understanding. Thank you!

[ahmadalghooneh]

Gilbert is the best, I love him, wish I had a teacher like that

[yimao]

When I learnt linear algebra in college, I couldn't understand why I need to learn it besides it was required. Profs Gibert Strange made it more meaningful and helped me understand its application in practice. All the pieces I learnt are now connected.

[alexz]

Each time, when I have the question about algebra, I always come to look for the answer in these lessons of Prof Gilbert. Thank you, Prof Gilbert.

[gauravrudramalik]

Thank you so much Prof. Strang, and sincere gratitude towards MIT for an initiative like the OCW.

Blessed are those who have the motivation to develop their skills in their younger years, and make it to an institution like MIT... but yeah, with uploads like this... even people like me can continue to develop our knowledge and understanding.
I am so glad and grateful to have an opportunity like this!

[benhaze]

This is so elaborately explained, yet so easy to understand
This is what teaching should look like!

[lowerlowerhk]

"how to I get hold of U?"- Gilbert Strang

[univuniveral]

When I was in Scandinavia, studying computer science, our textbook was by this same guru, Gilbert Strang. That book was pretty compact and perfect.

[dhaneshprabhu]

This prof is just amazing. In our college, only the formula and a large sequence of steps were mentioned to find SVD. I had a hard time comprehending it. This legend just mad eme understand SVD in just 2 equations with full concept. I wish I was born next to MIT. Thanku prof for enlightening me. And Thanku MIT OCW for making these vdos available

[piaopiaokeke]

Gilbert Strang has aged like fine wine! We will have lost a real gem when he is gone. His teaching is amazing.

[BalajiSankar]

thank you for showing that SVD is actually getting the different layers of the matrix out .. from the most important to the least important..