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: ruclips.net/video/7Tk6BAJ3mm8/видео.html
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. :)
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.
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.
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.
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 RUclips 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?
@@datamlistic I think title "Eigendecomposition Explained" open to interpretation, it could be understood as "Eigendecomposition (the process) Explained" or "Eigendecomposition (the resulting factors) Explained".
@@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.
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: ruclips.net/video/7Tk6BAJ3mm8/видео.html
Wonderful collection of videos! Thank you very much
Thanks! Happy to hear to you like the content I create on this channel. :)
Thanks for making this video! This actually made sense to me
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. :)
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.
Agreed :)
Nice explanation, thanks!
Thanks! Glad it was helpful!
Very well explained! Thanks :))
Thanks! You're welcome! :)
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.
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.
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.
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 RUclips 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?
@@datamlistic I think title "Eigendecomposition Explained" open to interpretation, it could be understood as "Eigendecomposition (the process) Explained" or "Eigendecomposition (the resulting factors) Explained".
@@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.