I subscribed! Martjin, you are an excellent teacher. Now, I'm gonna check your other videos. You teach some next-level topics.
@ashar41218 ай бұрын
Watching from Zürich, this is so great! You should have more subscribers
@lauragaleraalfaro80862 жыл бұрын
This video really helped me to understand givens rotations. Thank you!
@karol21002 жыл бұрын
Great video, thank you for everything. Watching from Poland (saying this just to empemphasize that your video is helpfull around the world)
@martijnanthonissen2 жыл бұрын
That's great to hear. Thanks for letting me know Karol!
@Schooling20236 ай бұрын
this is so great! Thank's
@TheLeontheking2 жыл бұрын
Small correction: at 11:00 the latter vector should be (sqrt(5), 0, 3) It's obvious from the equations listed afterwards though :)
@martijnanthonissen2 жыл бұрын
Yes! You are right. Thanks for commenting
@andrapi60242 жыл бұрын
Great explanation! Thank you!
@momentouscrazynoob17092 жыл бұрын
Thank you so much, I finally understand this concept!!
@martijnanthonissen2 жыл бұрын
Great to hear that. Thanks for your message!
@mxyptlkk11 ай бұрын
Thank you professor
@jahanvi9429 Жыл бұрын
thank you very much , it was helpful
@holyshit9222 жыл бұрын
Here it is easy to derive multiplications by Givens rotations and write it in the code When I mulitiplied A by G from left to get R i noticed that multiplication changes only two rows (labeled p and q in this video) When I mulitiplied I by G from right to get Q i noticed that multiplication changes only two columns (labeled p and q in this video) I also wrote this system of equations from which I got values for c and s Yes there is 1/2n(n-1) multiplications but single multiplication can be done just in one loop in O(n) time so both Givens rotations and Householder reflections are O(n^3) they differ only by constant If you try to compute roots of polynomial equations by eigenvalues method (it is numerical procedure and Givens rotations can help to find QR decomposition) (I know that it is space costly and there is a problem with repeated roots but some programs like Octave or packages like numpy use this approach) two of the companion matices are in upper Hessenberg form and two of them are in lower Hessenberg form In this case it seems that there is no difference between Givens rotations QR decomposition and Householder reflection QR decomposition
@martijnanthonissen2 жыл бұрын
Thanks for your comment! You often see a preference for Givens rotations when a matrix is “almost” upper triangular: if you have a matrix in upper Hessenberg form (upper triangular plus one lower diagonal) then you can use n-1 Givens rotations to just make the lower diagonal zero
@franciscoleandrosilvadelav1742 жыл бұрын
Thank you!
@heidioid2 жыл бұрын
Bookmark guided example 9:33
@fareoadewunmi88353 жыл бұрын
Great lecture! Thank you
@martijnanthonissen3 жыл бұрын
Glad you like it! Thanks!
@takudzwamashamba74532 жыл бұрын
woah thanks !!
@oafccouchpotato2 жыл бұрын
very well explained
@m.pranavphanindrasai24732 жыл бұрын
It was very clear Sir Thank you . Which book did you take for reference ??
@martijnanthonissen2 жыл бұрын
Thanks! I quite like the book "Scientific Computing" by Gander, Gander and Kwok
@recognize1992 Жыл бұрын
thank you for the lecture :) I have one simple question. why givens rotation matrix is a form of [c s;-s c] instead of [c -s;s c] despite the latter is a rotation matrix?
@martijnanthonissen Жыл бұрын
You can do both: one is a rotation in clockwise direction, the other is a rotation counterclockwise. Or, formulated differently, one is a rotation over an angle phi, the other is a rotation over -phi
@prvizpirizaditweb2324 Жыл бұрын
the only thing i did not understand was, why do we make g array that will not touch first , second or third entry, how this rule is applied?
@martijnanthonissen Жыл бұрын
Thanks for your question! Which slide or which time point in the video is it related to? I am not sure what it is that you are asking, so please let me know
@user-dl9no7jb4b2 жыл бұрын
May I ask how the matrices of G1, G2, and G3 are formed? I don't quite understand the position change of c s -s c .
@martijnanthonissen2 жыл бұрын
Thanks for your message! Say you would like to create a zero entry in the first column in row k. Then you need a rotation in the (1,k)-plane. The locations of the c, s, -s and c entries follow from the position (1,k). The main idea is that you make the (1,k) entry zero. However, you need to preserve the length of the first column, so you also change the (1,1) entry. Hope this helps!
@user-dl9no7jb4b2 жыл бұрын
@@martijnanthonissen Thank you!! I got it!!
@intansherlin49942 жыл бұрын
Where could I find the slides on Givens rotations, Prof. Anthonissen?
@martijnanthonissen2 жыл бұрын
I added a link to the slides in the description. Thanks for asking!
@intansherlin49942 жыл бұрын
Your welcome, Professor! Thank you for making linear algebra easier for me to comprehend 👍
@ajayiakinola9672 Жыл бұрын
is there a mistake at G1.A row1-column 1? it should be 5/sqrt(5)?
@martijnanthonissen Жыл бұрын
That’s the same, right? In the video I write sqrt(5), which is 5/sqrt(5)