So, the eigenvectors of a circular matrix are roots of unity -> Fourier matrix. I've used Fourier Transform and DCT in image processing and found it amazing but mysterious: where did it come from? Now I know. I also never realized convolution is essentially polynomial multiplication... and circular convolution simply applies a modulus to the powers! Mind expanding; thanks Prof Strang!
@exoticcoder53659 ай бұрын
to be precise, the eigenvalues of the above circular matrix are the roots of unity, Fourier matrix = eigenvectors corresponding to those eigenvalues
@RAJIBLOCHANDAS Жыл бұрын
Amazing! It's a real joy to follow Prof. Strang's lectures.
@ethanjensen15644 жыл бұрын
Gilbert Strang, you have done so much to help me learn linear algebra for my research. Thank you!!
@drewsam63873 жыл бұрын
Sorry to be offtopic but does anyone know a tool to get back into an instagram account?? I stupidly forgot the login password. I would appreciate any help you can offer me
@azariahivan39393 жыл бұрын
@Drew Sam instablaster ;)
@drewsam63873 жыл бұрын
@Azariah Ivan Thanks so much for your reply. I found the site on google and I'm trying it out now. Looks like it's gonna take quite some time so I will get back to you later with my results.
@drewsam63873 жыл бұрын
@Azariah Ivan It did the trick and I now got access to my account again. I am so happy:D Thank you so much, you saved my ass !
@azariahivan39393 жыл бұрын
@Drew Sam Glad I could help :D
@mahmudshamim1437 Жыл бұрын
One of the most amazing thing about MIT classes is, no matter how difficult questions peofesssor ask in a class, there are students who knows the answers.
@divyathangaraj92652 жыл бұрын
Thank you so much for the beautiful ideas behind the circulant matrices. Geometric ideas help me to understand the concepts easily, thank you.
@sandyjr5225 Жыл бұрын
Prof Strang, thank you so much for all your lectures.
@adamodimattia2 жыл бұрын
The legend! Thank you!
@georgesadler78302 жыл бұрын
Professor Strang, thank you for explaining the Eigenvectors of Circulant Matrices ,Fourier Matrix and their impact on Machine Learning.
@amesoeurs Жыл бұрын
why do you just copy and paste the title on every single one of these videos?
@exoticcoder53659 ай бұрын
@@amesoeursI don’t see there is a problem, he just wants to leave comment on each video to support the professor’s channel by boosting the algorithm
@Enerdzizer4 жыл бұрын
Interesting facts about normal matrices!
@vaghawanojha84455 жыл бұрын
at 51:00 did he mean e^(8*pi/3) which would be 1 instead of e^(6*pi/3)?
@tapioms4 жыл бұрын
No! is in facto because e^(6 pi/3) =e^(4 pi/3)*e^(2 pi/3)=e^(4 pi/3+2 pi/3)
@jerrymahone3355 жыл бұрын
Dr. Strang I see this matrix from a finite point of view. W is a generator 7 and P is 49 with a range 1 to p-1. 7^8 = 5764801, 5764801 / 48 = 120100.0208, 120100.0208 - 120100 = .0208 3333, .02080333 (48) = 1. I suppose this matrix is part of a discrete log problem. finding the exponent in Zp^*. this matix looks awfully close to the array for finding primitive roots. If so would numerical sequences that do not have a repeating pattern of numbers be Eigenvalues. Could you bring this cluster mess all together and show the short cuts.