Linear Systems of Equations, Least Squares Regression, Pseudoinverse

This video describes how the SVD can be used to solve linear systems of equations. In particular, it is possible to solve nonsquare systems (overdetermined or underdetermined) via least squares regression and the pseudoinverse.

These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[dragoncurveenthusiast]

This is so cool!
When I started this lecture series in order to understand PCA better, I had no idea it would also relate to least squares regression! This blew my mind!
Thank you so much for making these. They must be a lot of work, but they are so appreciated!

[PunmasterSTP]

Pseudoinverse? More like "Super videos for us!" Thank you so much for making all of them.

[idkravitz]

Am I right, that you write on real glass in front of camera and the image is just mirrored by editing? If so its brilliant.

[leofun]

I'm always impressed by how clean the board is, so it looks like there's nothing at all.

[neoblackcyptron]

Thank you for explaining hard to grasp concepts in a filtered simple manner for us to understand. Your lectures are a great complement to prof strangs both high quality content.

[macmos]

please keep going with the numerical linear algebra/numerical analysis/scientific computation/applied math stuff thanks :)

[EngineeringChampion]

Since A has fewer rows than columns, then A is an m×n matrix with m<n. Minutes 3:03 confused me for a while. Thank you for your great videos!

[reihanehvafadar]

can't thank you enough for sharing your knowledge with entire world

[philmccavity]

Exceptionally clear explanation, crisp hand-written notes, wonderful!

[chengkeattan]

Thank you very much for the clear explanation of pseudo-inverse.

[d_chip]

My god, you just explained what my professor is trying to explain for 5 lectures

[mauzaomin]

Thank you Steve for video. We make the assumption that it is an economy SVD at time 6:28. Then, how can we guarantee that V multiplies with V* will become identity matrix, especially for the under-determined system?

[utatistics]

having second thoughts about doing master cuz your videos are just too helpful

[pranjalsahu]

Excellent Lecture ! So clear to understand! Thank You !

[maettu]

Thanks for the video was really nice! There are 2 points which seem to be important to me. The invers of Σ is actually not always computable (if there exist a single value =0) so the more nice Expression would also be Σ+ . Where Σ+ is the matrix where every non zero single value is inverted but the zeroes are left as they are.

And why not follow the convention of naming matrizes? Normally a matrix is called a mxn matrix. It seems you use a nxm matrix here which i think is a bit confusing at first glance.

[amodamatya]

Thank you Professor for this valuable lecture

[noahbarrow]

knowing that the pseudoinverse exists makes me feel really powerful

[ehkim]

This is really nice lecture I've ever seen. I want to recommend this lecture for engineering graduate student basic class!! :-) Thank you so much~ I'll buy the book! ^-^

[lama]

In the case of over-determined matrix X, why VVT is equal to identity since we are using economy matrices?

[georgeyu]

i know this is just about the notation, but i think the majority of linear algebra text use m by n, rather than n by m. It's sometimes a little confusing here...