Regression and Ax = b: Over- and under-determined systems 

I ABSOLUTELY LOVE THE WORK YOU AND STEVEN BRUNTON HAVE DONE!!!! YOU ARE LEGENDS!!!! LOVE YOU!

He's setting a new standard for teaching Linear Algebra. He's GQ dress with the suite too. Enjoy the lectures they are Golden.

This channel is great! keep up the great work, fundamentally changing civilization.

Great stuff thanks a million professor Kutz. It is precise and concise, I can't imagine the number of souls you guys are saving out there

First comment. I admired the Dr. Kutz. And this video is grateful. Thanks Dr. Kutz

thank you Prof. Nathan Kutz

The best quality education

thank you for a wonderful book and video series

Thank you for the effort

Respect you

How does solver determine which variables are useful in case of l1 norm? Also, how do we prove theoretically that l1 promotes sparsity? Anyone?

GREATTT!

how do you do that?

Thank you very much Nathan for the great video! When in 3:37 you say "you cannot satisfy Ax = b, is overdetermined", if I imagine the case where some rows may be duplicated in my data or for some reason some rows happen to be a linear combination of the others I may get a "tall" matrix (or and overdetermined system) that may have a solution/s. In short, following the same definition of overdetermined as in en.wikipedia.org/wiki/Overdetermined_system, you can have an overdetermined system with a solution. Do you use a different definition of under- overdetermined? (for instance, only taking into consideration the number of equations after reduction?) or you are just focusing on what you assume to be the most common case in a data matrix (to not present duplicated or dependent rows? Thank you for the clarification =)

👍

The MathLab and Python solutions for the undetermined case, panel (D) do not match.