Least squares using matrices | Lecture 26 | Matrix Algebra for Engineers

[@ProfJeffreyChasnov]

Find other Matrix Algebra videos in my playlist kzbin.info/aero/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx

[@johnadams6249]

This is a great overview of the problem! A teacher of mine went over the steps without all the justification, so this was very helpful!

[@area51xi]

Wow. I was initially skeptical when I started watching thinking this is just another video on this topic. I already knew this material but now I know it much better. Very clear explanation. Thank you.

[@liambaldwin6823]

What an incredibly intuitive explanation!

[@ElizaberthUndEugen]

Ax = b in general has no solution here, since b is in an n-dimensional space and Ax is in a 2-dimensional (at most 2) subspace of that space, since Ax is a linear combination of 2 n-dimensional vectors. Just for anyone else that got stuck there for a moment.

[@harshvardhanranvirsingh9473]

Sir, you are amazing! This is by far the best at least according to me a best explanation for least squares optimization problem.

[@sanjogkarki7999]

Great video to quickly review the concepts. Thanks Jeffrey.

[@weisanpang7173]

At 7:17, you said "if AX equals B is overdetermined, that means B is not in the column space of A, there's no solution to X". Where does that come from ?

[@ArmstrongNigere]

great video , finally understand clearly the topic

[@area51xi]

I think what makes this topic confusing for beginners is that the x vector in Ax=b does not represent the "x's" but rather represents the betas. And the b in Ax=b does not represent the betas but rather the y's. It is an unfortunate accident of the nomenclature.

[@ProfJeffreyChasnov]

That would be a beginning beginner.

[@jackieliu1472]

@@ProfJeffreyChasnov me is a beginning beginner ^o^ ty for the great lectures

[@Flannel_girly]

you are the best!!!

[@michaelumitbozdemir3185]

You are a legend 👍

[@CRISTIANO18786]

it's not necessary that an overdetermined system has no solutions, it is unlikely in a real world scenario but it's not necessarily the case. If the columns of an overdetermined matrix are dependant for example in the 2D case then they lie on a line. my point is that the fact that there is no solution is not because the system is overdetermined but because b happens to not lie in the column space

[@benjellounyassine8646]

Very helpful, thank you

[@zhou6075]

thank you

[@martinsanchez-hw4fi]

In 7:15. If Ax=b it is not true that this implies that b does not lie in the collumnspace of A. It may be overdetermined and have a solution.

[@ProfJeffreyChasnov]

We are doing the least-squares problem here.

[@max.hastings]

Is this dude really out here writing backwards

[@10bokaj]

or maybe some tech has been made that can flip a video (omg what has the world come to)...

[@Peter_1986]

I think that he is recording himself behind a transparent wall, and then he reflects that recording around the vertical axis.

[@cathyfeng3385]

or he's writing on a mirror and the video might be everything in the mirror

[@max.hastings]

@@cathyfeng3385 writing on glass and then flipping video horizontally

[@charliehou9553]

TENET

[@sollinw]

great!

[@anselmo2194]

Nice sir

[@wallyduboss9464]

you lost me at Ax =b. . you have x under B and B1, A under X and b under the y's. If y=Ax +b, isn't what you wrote confusing?