Part 5: Singular Values and Singular Vectors

A Vision of Linear Algebra
Instructor: Gilbert Strang

Data matrices in machine learning are not square, so they require a step beyond eigenvalues: The Singular Value Decomposition (SVD) expresses every matrix by its singular values and vectors.

License: Creative Commons BY-NC-SA

[jeremyclark]

"Triangular matrices were good when we were young... An hour ago"
I love this guy

[CS-enuo]

wow when I was an undergrad years ago I learned linear algebra from Prof Strang's open course, now years later I'm a data scientist and watching him reviewing and emphasising SVDs and all these data science applications. Thank you professor, be safe.

[gbeziuk]

Thank you, professor! Be safe, live long.

[waldenli]

I was a bioscience major and was taught LA first year in college. I came across your open course one or two years later and somehow followed it along when it had nothing to do with the stuff I was dealing with in college, or anything concrete I was imagining. It just felt good to learn with you, and to understand things in a much better way. Linear algebra always gives the feeling of everything coming together after one goes through it. Well, still, I forgot them all, because I rarely used them. Later I studied something about dynamics of differential equations, and realized how neat eigenvalues are. Now you reminded me that SVD is what PCA is all about. Thank you Prof. Strang. Everyone who followed your courses could see that you care about students' learning, and because your heart is there, you know how to present things and the pace it should take. Maths can have flesh and blood after all.

[fawzibriedj]

Thank you very much Pr. Strang, it's a pleasure to watch these videos!

[azamatdevonaev]

Stay well, prof. Strang. You are one of the best lecturers in this whole universe

[sameeryear]

You are amazing sir. I have become fan of the way the way you teach. I was struggling since a lot of days to really understand Eigen-decomposition and SVD but nobody explains it as beautifully as you did.

[ther]

This isn't for people who know nothing about LA. You have to learn LA first and then come back to these to get the "2020 Vision" on LA.

[echolee]

Thank you for these amazing videos！Expecting the new book in 2021🥳🥳

[MsKouider]

Thank you very much Professor STARNG, very clear and deep explainations! only a very great scholar can do it. Sincere salutations from ALGERIA ALGEBRECLY YOURS: after THE FATHER OF ALGEBRA ALKHAWARIZMI YOU ARE THE BEST

[wb]

Thank you, Prof. Strang. I really benefit a lot from your courses.

[MrFischvogel]

Professor, you are a beautiful person.

[RC-bmmf]

Please be safe and good, Professor Strang. Thanks a lot for this great summary! Looking forward to meet the new book while I watch the good old lectures and hone my mastery on the great previous book of yours! - A big hug from Asia -

[aungkyaw]

Rotate-stretch-rotate . "Say it again" --- Remind me series of the individual row reductions matrices before putting them to the other side for LU. Thanks Professor.

[ethanlabelle]

Thank you Professor Strang! From a current 18.06 student!

[arkapravagoswami]

Long live sir & Teach us like this...

[Sam-zgvc]

Thank you Professor for this beautiful lecture..

[arpitdwivedi]

Lots of love....
Thank you for this.

[vishwapriyagautam]

I never understood why does he always tell that the vi's are in the row space of A?

[Tiaraz]

Can we please get a detailed answer key to some extent for (odd or even questions) for the new book expected in 2021. Even if it’s for purchase I would be willing to buy it. Detailed solutions help out tremendously especially in showing exactly why a question is done in such a way. Thank you!