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.
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.
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 ?
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.
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
Find other Matrix Algebra videos in my playlist th-cam.com/play/PLkZjai-2Jcxlg-Z1roB0pUwFU-P58tvOx.html
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!
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.
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.
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 ?
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.
That would be a beginning beginner.
@@ProfJeffreyChasnov me is a beginning beginner ^o^ ty for the great lectures
What an incredibly intuitive explanation!
Sir, you are amazing! This is by far the best at least according to me a best explanation for least squares optimization problem.
Great video to quickly review the concepts. Thanks Jeffrey.
great video , finally understand clearly the topic
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
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.
We are doing the least-squares problem here.
you are the best!!!
Is this dude really out here writing backwards
or maybe some tech has been made that can flip a video (omg what has the world come to)...
I think that he is recording himself behind a transparent wall, and then he reflects that recording around the vertical axis.
or he's writing on a mirror and the video might be everything in the mirror
@@cathyfeng3385 writing on glass and then flipping video horizontally
TENET
You are a legend 👍
Very helpful, thank you
thank you
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?
Nice sir
great!