Although powerful, the eigendecomposition can be used only to factorize square matrices. To overcome this limitation, the singular value decomposition (SVD) was invented. Check out the explanation here to learn more: kzbin.info/www/bejne/bYXOZ3V3f5igo5o
@nicolascortegosovissio28244 ай бұрын
Wonderful collection of videos! Thank you very much
@datamlistic4 ай бұрын
Thanks! Happy to hear to you like the content I create on this channel. :)
@Kazshmir8 ай бұрын
Thanks for making this video! This actually made sense to me
@datamlistic8 ай бұрын
Thanks for the feedback! I am really happy you enjoyed it and understood the explanation! Please let me know if you think I could have done something better. :)
@DimitrijeĆirić-x1x7 ай бұрын
Nice explanation, thanks!
@datamlistic7 ай бұрын
Thanks! Glad it was helpful!
@ricardoveiga0074 ай бұрын
Very well explained! Thanks :))
@datamlistic4 ай бұрын
Thanks! You're welcome! :)
@varshak93256 ай бұрын
To use eigen decomposition method for finding A^p, we also need to find U and U^-1 , which makes it a little bit lengthy . However it's usefull when p is very large.
@datamlistic6 ай бұрын
Agreed :)
@AkiraTheCatgirl04 ай бұрын
Isn't this the same as diagonalization? We find a basis of the eigenvectors of A, then find what A looks like in that basis.
@datamlistic4 ай бұрын
Yes, they are mostly the same. Actually A has to be diagonalizable in order to be able to eigen decompose it. The only difference I see is the end results: a diagonal matrix that represents the gist of A for diagonalization, and the decomposition in terms of eigenvectors and eigenvalues for eigen decomposition.
@AntiProtonBoy8 ай бұрын
Interesting video, but it seems to focus on the application of decomposed matrices, instead of explaining how to actually perform such decompositions. The video appears to makes the assumption that the factorised quantities U and Λ are already known.
@datamlistic8 ай бұрын
Thanks for the feedback! Well, the eigendecomposition is based on extracting the eigenvectors and eigenvalues of that matrix, and I didn't want to dig too deep into that because that's a well covered topic on KZbin and on other platforms in general. However, I've tried to provide a brief proof of how you can obtain the eigendecomposition at 1:33. Isn't this enough to understand how this decomposition is performed? Am I missing something?
@AntiProtonBoy8 ай бұрын
@@datamlistic I think title "Eigendecomposition Explained" open to interpretation, it could be understood as "Eigendecomposition (the process) Explained" or "Eigendecomposition (the resulting factors) Explained".
@MalikMehsi7 ай бұрын
@@AntiProtonBoy Tbf I think when you teach something like Eigendecomposition one should already now the fundamental basics of what Eigenvectors and Eigenvalues are and how to extract those from a matrix.