Thank you so much i could do the exams well but never really fully understand why, simply memorised all the formula and cases, it was such a pain...until your lecture. it feels that I had been sick but finally got cured. Thanx
I struggled to actually understand what decomposition was all about (let alone eigenvalue decomposition). Thanks so much for making it cristal clear! You sir are definitely the best!
Thank you. The explanation is very clear. The sound and tone are very good. I like the fact that you started with numbers and specific example. Thank you.
How did you get the eigen vectors if someone can explain, I got the first eigen vector by gaussian elimination, however struggling to get 2nd and 3rd eigen vector for 4 and 3.
it's better to explain why the eigen-vector matrix times the eigen-value matrix is equivalent to the eigen values on a right-matrix(eigen-value matrix) time the columns on a left-matrix(eigen-vectro matrix) because intuitively that's not how the matrix multiplication works. In fact, it looks that way because the right-matrix is a diagonal matrix.
Starting at 4:53 when converting the 3 separate vector equations into a single matrix equation, how do you know in which order the eigenvalues (7, 4, 3) lie diagonally in Lambda matrix shown at 5:21? If you skipped some steps, could you please explain the work?
The order of eigenvalues along the diagonal of its matrix must match the (column) order of eigenvectors in its matrix. You can reverse the order of the eigenvalues, but then you must reverse the order of the eigenvectors as well.
No doubt I would not have this question if I had followed your entire course, but can you tell me why it is immediately obvious to you that 4 must be an eigenvalue simply by virtue of the fact that (1) it is the only nonzero value in column 3 and (2) it is on the diagonal? What is the reasoning behind that? I wish I knew more shortcuts like that for finding eigenvalues!!
Consider an orthonormal basis e1,e2,e3 (unit vectors). The last column contains the coefficients of the vector (say a1) obtained when the matrix A acts on the unit vector e3. so : a1 = Ae3 = A13 e1 + A23 e2 + A33 e3. Since A13 and A23 are zero, Ae3 = A33 e3, this implies A33 is one eigen value and e3 the corresponding eigen vector of matrix A.
around the 5 min. mark:: this should get (v_3)(l_3) =[-3 3 15] but the last column for "A times 3rd eigenvector" should be (A)(v_3)=[-3 3 25] so they are not equivalent. Whats happening? did i mess up?
That's fair. This video is part of a series and might not make sense out of context. Here's Part 3 of the overall series which will put this video in context.
Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.
Thank you so much i could do the exams well but never really fully understand why, simply memorised all the formula and cases, it was such a pain...until your lecture. it feels that I had been sick but finally got cured. Thanx
you are awesome man, I havent had the time to check all your videos but I will soon, thank you very much for doing these
I struggled to actually understand what decomposition was all about (let alone eigenvalue decomposition). Thanks so much for making it cristal clear! You sir are definitely the best!
Hi Vicente, thank you for letting me know - it's much appreciated. -Pavel
Thank you. The explanation is very clear. The sound and tone are very good. I like the fact that you started with numbers and specific example. Thank you.
thank you professor
Thank you - glad you enjoyed it!
That was beautiful
Saved it in my playlist
Glad you liked it!
Thank You !
Glad it was helpful!
How did you get the eigen vectors if someone can explain, I got the first eigen vector by gaussian elimination, however struggling to get 2nd and 3rd eigen vector for 4 and 3.
Solution of the question is clear... Gr8 lect
a similarity transformation, of the matrix LAMBDA.... haha, I enjoyed that edit. Thanks so much for this informative video!
Thank you! Glad you enjoyed that!
Simply beautiful.
Thank you for the feedback!
This is so beautiful. Thank you!
Great Lecture. His explanation is very straightforward.
Thanks ,it helps me understanding the deep learning by Goodfollow
I think you refer to Ian Goodfellow
Hahaha I am reading that book as well
amazing , wonderful! thank u very much ,
Thanks, much appreciated.
it's better to explain why the eigen-vector matrix times the eigen-value matrix is equivalent to the eigen values on a right-matrix(eigen-value matrix) time the columns on a left-matrix(eigen-vectro matrix) because intuitively that's not how the matrix multiplication works. In fact, it looks that way because the right-matrix is a diagonal matrix.
Thanks so much for these wonderful, clear video!
fantastic video, thank you very much!
Well explained.
Thank you - glad you found it helpful!
Starting at 4:53 when converting the 3 separate vector equations into a single matrix equation, how do you know in which order the eigenvalues (7, 4, 3) lie diagonally in Lambda matrix shown at 5:21? If you skipped some steps, could you please explain the work?
The order of eigenvalues along the diagonal of its matrix must match the (column) order of eigenvectors in its matrix. You can reverse the order of the eigenvalues, but then you must reverse the order of the eigenvectors as well.
2:20 I didnt understand how you got the third eigenvalue. I'm kind of new at this. Can somebody please explain?
You do great videos keep it up!
Well Done
thank you
grazie
merci
شكرا
gracias
Great video!
great explanation! Thanks alot!
No doubt I would not have this question if I had followed your entire course, but can you tell me why it is immediately obvious to you that 4 must be an eigenvalue simply by virtue of the fact that (1) it is the only nonzero value in column 3 and (2) it is on the diagonal? What is the reasoning behind that? I wish I knew more shortcuts like that for finding eigenvalues!!
Maybe you won't need it after 2 months, but the sum of the values on the diagonal(that's the trace) must be equal to the sum of the eigenvalues.
Consider an orthonormal basis e1,e2,e3 (unit vectors).
The last column contains the coefficients of the vector (say a1) obtained when the matrix A acts on the unit vector e3. so : a1 = Ae3 = A13 e1 + A23 e2 + A33 e3. Since A13 and A23 are zero, Ae3 = A33 e3, this implies A33 is one eigen value and e3 the corresponding eigen vector of matrix A.
Very nice video, thanks teacher kane.
This is the 10x slow motion version of my prof lecture.
fantastic
around the 5 min. mark:: this should get (v_3)(l_3) =[-3 3 15] but the last column for "A times 3rd eigenvector" should be (A)(v_3)=[-3 3 25] so they are not equivalent. Whats happening? did i mess up?
I think you made a tiny arithmetic mistake. -4-1+20 = 15. I think you just flipped the minus signs and got 4+1+20 = 25.
Where is the video which shows how you computed the eigenvalues and eigenvectors
ruclips.net/video/2mPl3qKMFL4/видео.html
Bravo
thanks good vid
how did you find the eigen values?im confused
Thank you! :)
Suscribed!
Namaskaram Kane
Not understand anything
That's fair. This video is part of a series and might not make sense out of context. Here's Part 3 of the overall series which will put this video in context.
ABC kids
Thank you!