Part 3: Orthogonal Vectors
ฝัง
- เผยแพร่เมื่อ 30 มิ.ย. 2024
- A Vision of Linear Algebra
Instructor: Gilbert Strang
View the complete course: ocw.mit.edu/2020-vision
TH-cam Playlist: • A Vision of Linear Alg...
Professor Strang describes in detail orthogonal vectors and matrices and subspaces. He explains Gram-Schmidt orthogonalization, as well as the Least Squares method for line fitting and non-square matrices.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
For links to Professors Strang’s related courses on OCW, visit the Related Resources page on the full resource site: ocw.mit.edu/2020-vision.
LMAOO he never forgets dissing Schmidt
It's 2020 and Schmidt is still getting wrecked lmao
Ramon Massoni 😂
th-cam.com/video/XPCgGT9BlrQ/w-d-xo.html 👍💐💐
Graham has the idea, I don't know how Schmidt got into it... 18:06 Nostalgia
yes, it was in lectures too as far as I remember
I've just found out he's 86 this year. Such a legend.
This is the fourth video of the series I am watching. While I think I am familiar and comfortable with LA, I already learned some useful and interesting concepts and points of view from these lectures. BTW, this is how I imagine Mr. Rogers would teach LA, if Mr. Rogers were a math teacher.
Professor Strang is by far an incredible person and an amazing professor of mathematics.
I feel like watching Messi in his waning days when I am watching these videos of Strang. I used to watch his MIT videos back in 2010. We are blessed to still have you Pr. Strang.
I just love MIT OCW,
I request you, people, to make a playlist of organic chemistry...
10:07 In mind, "Let me write something. OMG! Where is my blackboard?" Miss your moving pieces of blackboard up and down many times in one session of the lecture, dear Professor.
Dear Gilbert. I adore you so much! Even when it seems i ought to use admire or to be infatuated by you, i stand by baby doll adoration for your straight out simple wonderful math explanations ❤️ ILU for teaching us. THANK YOU!
Unbelievable commentary. I was watching the videos out of order and thinking to myself “this guy is unusually good.” Then I heard him say his name.
The geometric illustration of least square is soooo cool👍👍
watch The Mathematics of Machine Learning by Zach Star at 2m20s - that what cool explanation of least squares is.
It appears that Egypt liked polar co ordinates
Note that there is a subtle "mistake" on the slide titled "Orthogonal matrix" (around 6:10). An example was presented where Q is the 2D rotation matrix, with eigenvalues exp(+ or - i \theta). The argument presented showing that |\lambda^2|^2 = 1 is true if the complex conjugate is taken at the same time as the transpose (^T) operation and if ||Qx||^2 and ||x||^2 are non-zero, so that these can be canceled from both sides. For the eigenvalues of the 2D matrix Q, obviously \lambda^2|^2 = 1. But if the complex conjugate is not taken with the transpose operation, ||Qx||^2 and ||x||^2 CANNOT be canceled from both sides since ||x||^2 = 0 for the 2D matrix Q.
Man u r so intelligent 🙄🙄🙄
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!
Detailed solutions are very bad for a math textbook (Since you can just skip having to think) .Hints are more preferable.
This dude's the OG of linear algebra.
A real master
Animated, Paced and Clear presentation.
The length of a vector (-1,2,2) at 4:20 would be the same as the length of a vector (1,2,2) which would be sqrt(11), not sqrt(9).
My vector says linear 9036
Professor Strang, Can you explain the limitations of least squares? When will the error vector be significantly large enough that it would nullify the method itself?
Here's my completely ignorant guess. Once 'e' becomes longer than 'p' the value of projection drops below 50%, as does your ability to predict x-hat.
The Godfather of Matrices...
Thankyou
Linear Algebra review day8
I love prof Strang, but I think the proof he presented is a great example of why (unfortunately) ppl don't like proofs. Yes it shows why things are true but I'd assume for most ppl it comes out of thin air. There is little motivation to how it would occur to someone how to do it. e.g. no motivation of how you'd even know in the first that orthogonal is a property to expect from symmetric. Even if we did expect it, how in a proof real ppl doing them think hmm I have this property transpose and I need to use it as a key step in the my proof...etc. It is just too magical without any motivation from how the result would be expect or the proof method itself would be expect. Just a random set of facts that worked. This is what I think has to change for ppl to stop hating proofs. Make them appealing to humans, rather than to computers. Where did they come from? Where did the technique used work? etc.
It's not a math journal (even then I think the above should apply), it's a class room.
👍👍👍👍👍👍👍👍👍
Spring Theory?! 🤔
Isn't it be string theory?
Why in 2:54 there is Q * Q^t != I ?
It does not have to be square matrix
Because the rows are not orthogonal to each other
We only call Q orthogonal matrix when Q is square because only when Q is square Q^t = Q^-1 (Q_transpose = Q_inverse)
I saw that. The ortogonal proposition is: Q*Q_t=I or Q_t=Q_1. But the slide changed the position. Is It correct?