Linear Algebra 18a: Introduction to the Eigenvalue Decomposition

  Рет қаралды 91,150

MathTheBeautiful

MathTheBeautiful

9 жыл бұрын

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Пікірлер: 57
@MathTheBeautiful
@MathTheBeautiful 3 жыл бұрын
Go to LEM.MA/LA for videos, exercises, and to ask us questions directly.
@Unidentifying
@Unidentifying 9 жыл бұрын
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
@denisebay1737
@denisebay1737 6 жыл бұрын
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
@maoyiluo8611
@maoyiluo8611 5 жыл бұрын
Thanks so much for these wonderful, clear video!
@diegowang9597
@diegowang9597 3 жыл бұрын
This is so beautiful. Thank you!
@TheGodSaw
@TheGodSaw 8 жыл бұрын
You do great videos keep it up!
@Mutageneofficial
@Mutageneofficial 6 жыл бұрын
fantastic video, thank you very much!
@Jeet_C
@Jeet_C 3 ай бұрын
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.
@alimuqaibel7619
@alimuqaibel7619 3 жыл бұрын
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.
@ParthSharma1996
@ParthSharma1996 8 жыл бұрын
Great video!
@severinmundl2710
@severinmundl2710 6 жыл бұрын
great explanation! Thanks alot!
@sakshimahajan7123
@sakshimahajan7123 8 жыл бұрын
Solution of the question is clear... Gr8 lect
@mateusmbr1
@mateusmbr1 5 жыл бұрын
Very nice video, thanks teacher kane.
@nackyding
@nackyding 4 жыл бұрын
Thank you!
@julianandressalazar5755
@julianandressalazar5755 Жыл бұрын
2:20 I didnt understand how you got the third eigenvalue. I'm kind of new at this. Can somebody please explain?
@travisblack9519
@travisblack9519 7 жыл бұрын
fantastic
@slowcummer
@slowcummer 8 жыл бұрын
Great Lecture. His explanation is very straightforward.
@mastrammeena328
@mastrammeena328 3 жыл бұрын
That was beautiful Saved it in my playlist
@MathTheBeautiful
@MathTheBeautiful 3 жыл бұрын
Glad you liked it!
@lalahaha3699
@lalahaha3699 4 жыл бұрын
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?
@georgeobrien1011
@georgeobrien1011 4 жыл бұрын
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.
@roach5429
@roach5429 Жыл бұрын
how did you find the eigen values?im confused
@weigthcut
@weigthcut 8 жыл бұрын
Thank you! :) Suscribed!
@tombouie
@tombouie 5 жыл бұрын
Well Done
@souravdey1227
@souravdey1227 3 жыл бұрын
Simply beautiful.
@MathTheBeautiful
@MathTheBeautiful 5 ай бұрын
Thank you for the feedback!
@xinking2644
@xinking2644 3 жыл бұрын
amazing , wonderful! thank u very much ,
@MathTheBeautiful
@MathTheBeautiful 3 жыл бұрын
Thanks, much appreciated.
@user-rb8oi5gj6c
@user-rb8oi5gj6c 5 жыл бұрын
thanks good vid
@pagames3d
@pagames3d 2 жыл бұрын
Thank You !
@MathTheBeautiful
@MathTheBeautiful 5 ай бұрын
Glad it was helpful!
@youmah25
@youmah25 9 жыл бұрын
thank you grazie merci شكرا gracias
@vicentefajardorosas3589
@vicentefajardorosas3589 2 жыл бұрын
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!
@MathTheBeautiful
@MathTheBeautiful 2 жыл бұрын
Hi Vicente, thank you for letting me know - it's much appreciated. -Pavel
@ArturHolanda91
@ArturHolanda91 5 жыл бұрын
Bravo
@littlerainyone
@littlerainyone 8 жыл бұрын
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!!
@zeon137
@zeon137 7 жыл бұрын
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.
@SAGARBODKHE
@SAGARBODKHE 7 жыл бұрын
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.
@pedromoya9127
@pedromoya9127 2 жыл бұрын
thank you professor
@MathTheBeautiful
@MathTheBeautiful 5 ай бұрын
Thank you - glad you enjoyed it!
@tifanyburnett1804
@tifanyburnett1804 6 ай бұрын
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?
@MathTheBeautiful
@MathTheBeautiful 5 ай бұрын
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.
@faktamerapu7743
@faktamerapu7743 4 жыл бұрын
This is the 10x slow motion version of my prof lecture.
@cedrickiplimo2991
@cedrickiplimo2991 2 жыл бұрын
Well explained.
@MathTheBeautiful
@MathTheBeautiful 5 ай бұрын
Thank you - glad you found it helpful!
@korvinking5027
@korvinking5027 6 жыл бұрын
Thanks ,it helps me understanding the deep learning by Goodfollow
@akhileshpandey8457
@akhileshpandey8457 4 жыл бұрын
I think you refer to Ian Goodfellow
@yuqiwang7829
@yuqiwang7829 4 жыл бұрын
Hahaha I am reading that book as well
@conjetapierre8755
@conjetapierre8755 4 жыл бұрын
Where is the video which shows how you computed the eigenvalues and eigenvectors
@MathTheBeautiful
@MathTheBeautiful 4 жыл бұрын
kzfaq.info/get/bejne/aNOAn5aisLOqfGg.html
@darklight1030
@darklight1030 2 жыл бұрын
a similarity transformation, of the matrix LAMBDA.... haha, I enjoyed that edit. Thanks so much for this informative video!
@MathTheBeautiful
@MathTheBeautiful 5 ай бұрын
Thank you! Glad you enjoyed that!
@howardguo398
@howardguo398 5 жыл бұрын
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.
@piyushmajgawali1611
@piyushmajgawali1611 4 жыл бұрын
Namaskaram Kane
@yuryperikov1783
@yuryperikov1783 4 жыл бұрын
ABC kids
@jatinkumar3246
@jatinkumar3246 7 ай бұрын
Not understand anything
@MathTheBeautiful
@MathTheBeautiful 5 ай бұрын
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.
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