Eigenvalue and Eigenvector Computations Example
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- Опубліковано 22 гру 2013
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Eigenvalues and eigenvectors play an important role in many signal processing applications. This example demonstrates the mechanics of computing the eigenvalues and eigenvectors of a specific 3x3 matrix. Eigenvalues are always the roots of the matrix characteristic equation, i.e. det(A-LI), while eigenvectors are found by finding the null space of the equation A-LI for each eigenvalue L.
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for everyone that is having exam tomorrow, good luck! :D
Today :)
Thenx, mine was yesterday, but thenx anyway bud.
my lecturer explained this badly and you made me understand within 20 minutes!!!
this helped me a lot!! thanks!!
Dear Adam, you have provided the best explanation to solve eigen vector....thanks a ton! God Bless You!
Glad I could help, thanks for the kind words! Make sure to check out my website adampanagos.org for additional content you might find helpful.
the ONLY problem with video was WHY WAS IT SO HARD TO FIND?! big THANK you! :)
AaaaaDddxz
Thank you so much, I finally understood how to get eigenvectors thanks to you!
Great, glad to hear that. Thanks for watching!
fantastic video. No assumptions, ground up approach, that i greatly appreaciate. very clear. thank you
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content you might find helpful. Thanks much, Adam
I also liked your exampel / presentation. When finding the eigenvectors corresponding to a given eigen value. It's normal to put z = t, where you write "any". The eigen vector would then for Lambda = 2: t x ( 1 -2 1), and visually expressing that you can scale the eigenvector just by choosing any number to the parameter t. Keep up the good work.
This is the only one and best one explained how to PROPERLY solve a eigenvalue and eigenvector in the whole WEBB! Thank you for solving a 3 x 3 matrix like this!
Glad you found it useful, thanks for the nice feedback!
Great question about eigenvalues Mayank.
You can read about MIMO communication here: en.wikipedia.org/wiki/MIMO
You'll note that the capacity of the MIMO channel is a function of a determinant that contains the channel matrix H. In general, H is modeled as a random matrix, so its eigenvalues are also random. This is important since the determinant of a matrix is the product of its eigenvalues. So, in this way, the eigenvalues of a wireless communication channel matrix are important since they determine the capacity of the channel. Hope that helps point you in the right direction.
Sir, you made the things much simpler to understand..!😀Great job, sir👍👍
Thank u big man. It's quite easy to just type eig(A) in matlab but would rather understand the concept behind it.
Thank you very much , helped me so much this semester
thanks alot for the help in eiglen values and vectors be blessed
literally the most useful channel on the internet! thank you soooooooooooo much!!!!!!!!!!!!!!!!!!!!!
Glad I could help, thanks for watching. If you’re looking for additional examples/videos make sure to check out my website adampanagos.org where I have a lot of other videos and resources available that you might find helpful. Thanks, Adam.
wow such an easy and brief methods he used to solve this problem. Loved his explanation and solving method. Thanks a lot sir
You're welcome, thanks for watching!
No you did't undersdand adytthin Vishmerayaahowdospeakvishnyshiva hireapartmentinhindi idiot!!!
This is the Best Video I found about eigenvalues and eigenvectors,You are a Great lecturer Mr Adam,Thanks for helping me :)
Glad to help, thanks!
You videos are always extremely helpful. Thank you!
+Gabrielle Birkman You're welcome, thanks for the nice feedback!
I really liked this presentation.
The scaling factor for the Eigen vector always confused me. Thanks for the clarifications!!!
that helped me a lot! thank u so very much!
Saved my life with this video thank you!
Glad I could help, thanks for watching!
It's my exam tomorrow, thank you for saving me
Glad I could help! I hope your exam went well!
Wow that was FLAWLESS! thanks a lot
Glad it helped, thanks for the nice feedback!
Actually, he messed up the last sentence.
very easy to understand sir ,thank u so much.
Clear and efficient presentation! Thanks!
+tlt You're welcome, thanks for watching!
thanks Adam you are the best teacher
Thank you this helped me alot.
wonderful finally i got it
thanks a lot!!
very nice explanation.
thank u.
You are the best teacher. Thanks a lot.
Thanks!
Great explanation sir
Watching at 1:30 AM.Test in the morning! You are a life saver !!
Glad I could help and hope your test went well!
thankz for the
clear picture.....
great work!!
thanks man you helped me so much this semester
+Charles Amofordjuoh Excellent, glad to hear that. Thanks!
Excellent that's called a perfect MATHEMATICIAN
Thank you very much sir.
Thank you sooo much for the eigenvectors. I not seen the logic behind them at all. Thanks!
Glad you found it useful, thanks!
Gave me 4 points on the exam ;D (of tot 24)
it's really good...!! I just got an easy way to solve the problem
Adam, this video's very helpful for me. Thanks.
I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam
Adam, this video is pretty solid, nice job. (This is Steve Malbasa.) Thank you kindly.
BIG THANK YOU
great job Man thank you so much
thanks.really helpful
easy to understand. thanks
Gr8 video n explanation too
thank you so much Adam, you really helped me in my maths 2 college subject
Awesome, glad I could help!
I hope you are doing your MSc or phD now :)
You saved my exam.. Cheers :)
Glad to help, hope the exam went well!
This helped a ton thank you!
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
Thanks man , you did such a great presentation , i am just wondering if can i use the same method to find the Eigenvector for 3x3 matrix with trigonometric basis .
Thanks mään, shut your mouth mään!! And don't smile!!! Thänks mään!!!
What happens if an entire column (not row, as you've shown here) ends up being 0. For instance if all y entries are 0, does that equate y to any value or something else?
What a beautiful video!
Thanks! Make sure to check out my website adampanagos.org for additional content you might find helpful. Thanks again, Adam.
good example.
I very much liked this video. I have done extensive searching but I didn't clearly understand the clear usage of Eigenvalue and Eigenvector in practical life. I somewhere read "it determines how much information can be transmitted through a communication medium like your telephone line or through the air or analyzes deformities in the building structure". But I don't understand how they create Eigenvalue and Eigenvector in such practical purposes. If you please give me some real life example that will be very helpful for me. Thanks in advance.
Thanks very much
Hello Mr. Adam
can you make a tutorial for jordan form representations in matrix 2x2 or 3x3? :) Thanks.
Thanks! And I really like your font!
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (450+ videos) you might find helpful. Thanks much, Adam
That was smooth.
I instantly got lots when your started the eigen vector
thank you so much for your help
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (435+ videos) you might find helpful. Thanks, Adam.
Thank you so much
fantastic!
thank you a lot Sir!
+franco diaz You're welcome, glad you liked!
Hi Dear Adam Panagos!
can you please help me regarding ''eigenvector centrality"... I am working on a network, having 278 different nodes.. by using R-project I found results... eigenvector column --> ranging from 0.14 to 1 and eigenvalue column contains same value (183.44) against all 278 nodes. ... now needs to interpret... can u help ?
Very helpful.. thanks alot
You're welcome, thanks for watching!
بارك الله فيك رائع ما شاء الله
Thanks for the kind words, thanks for watching. Best,
Adam
easy to understand, thanks sir
You're very welcome, thanks for watching.
Thank you
Perfect!
how do u know which eigenvalue is 1, 2 or 3
wonderful
this is an excellent video. do you not have anything on the Gram-Schmidt algorithm?
Glad you liked the video. Sorry, I don't have anything right now on the GS algorithm. Hopefully I'll get around to something like that in the future. Thanks.
sir please answer me this
after getting the final equation you changed the signs of the equation in the eigen values
why????????????????????????????????????????????????????????????
You made it easy like 1+1
hi thanks for this video. i got stuck in part b in finding null space of A. please explain where E3 = 2E3 + E1 comes from. thank you very much
The eigenvectors are found by solving the null space equation. After we let L1 = 0, we end up with a linear system of equations. We need to solve this linear system of equations. To solve it, I used the Gaussian elimination method (i.e. row reduction method) to manipulate the system of equations into a form that I could more easily see the solution. The equation E3 = 2E3 + E1 didn't really "come from" anywhere, it was just a step I performed to solve the system of equations. We can always take linear combinations of equations without changing the solution to the system of equations. This just happened to be one linear combination I found useful since it introduced a 0 into the 3rd row and first column of the matrix. There are certainly other sequences of steps that would help you get there as well. Hope that helps.
wtf youre actually so lit at explaining everything
Thanks much, glad I could help!
Adam thanks for this video . It really helps me but i have a ques. After putting eigen vector matrice become
-0.5 1
2 -3.5 How can i find eigen vectors
Did you watch the last half of the video? In the first part of the video I solve for the eigenvalues. In the last half of the video I solve for the corresponding eigenvectors. You can follow the same process to compute eigenvalues and eigenvectors for any matrix.
Hi, thanks for your wonderful videos. I need examples for LU Decomposition of a matrix and Gaussian Elimination. Is there any? I cannot find them in your videos.
You're very welcome. Sorry, I don't think I have any on those. I have like ~70 linear algebra videos but none on those topics yet. Guess I need to add those to the list!
Really good stuff.
Thanks!
All of your 3 Eigen values formed a system in which the last row was all zero so you got the chance to select one variable to be any.
What if (after row operations) your system has all diagonal values non-zero; in that case what would be your steps?
You will always get a row with all zeros. That's the definition of an eigenvalue that det(A-LI) = 0, so you'll always have a free variable and a row of zeros. Hope that helps,
Adam
Thank you!
You're welcome, thanks for watching!
Sir, but how do i calculate the eigen values if there is also a constant in the equation(with the lamda values as well)?
If you need to compute the eigenvalues of a matrix that contains variables (as opposed to the numerical values as in this example) you would still follow the same process: Compute the characteristic polynomial and find the roots of the polynomial. These roots are still the eigenvalues. The only difference will be that these roots are function of the variables in your starting matrix (as opposed to numerical values). Hope that helps.
Thank you :)
i got A in first Midterm and the i got F in the second Midterm and now its new year everyone is having fun and im studying to atleast end up with B
Good luck! Hope your exam went well!
Why would you do row reduction to find your eigenvectors if you could just do a system of equations? Or do I have this thinking backwards since avoiding system of equations is the point of matrixes
Thanks a lot :) Its surely gonna be useful
Glad you liked it, thanks.
Great Sir.
I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam
awesome stuff, have you got more tutorials??
Glad you liked the video. If you're looking for more I have about 170 or so videos on my UA-cam page (ua-cam.com/users/agpanagos) that you can check out. I also have these videos organized on my personal webpage (www.adampanagos.org) in more of a "course-organized" manner.
Very good man 💜
Thanks for the kind words. Make sure to check out my website adampanagos.org where I have a lot of other videos and resources available that you might find helpful. Thanks, Adam.
Thank you so much for sharing this to make me understand more ：)
Awesome
Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam
please find eigen value of 5 * 5 matrix
super !!!
Presentation ❤️
When you manipulated the matrix, is it in echelon form or reduced echelon form? I'm kind of confused when it comes to these two forms.
+Jackji WangHeo Technically, the form I manipulated these into was echelon form, not reduced echelon form. The two forms are VERY similar, but reduced echelon form has every leading coefficient of a row equal to 1, while the row echelon form can have other numbers.
You can read more about the slight difference between these two forms here:
en.wikipedia.org/wiki/Row_echelon_form
For this problem, it doesn't really matter exactly what form we manipulate it into. The key thing was being able to perform operations to be able to solve the system of equations.
Hope that helps.
Hi Adam, very nice and useful video.
Sorry about the silly question, I would like to know what software are you using to create this video (with matrices, math functions, etc...) Thanks a lot...
I use an iPad app called Doceri (www.doceri.com) for most of my videos. This app lets you record all your handwriting ahead of time and use "breakpoints" to pause as needed. Once all the writing is down you can "play" the handwriting back while recording audio over it. I find this works much better than trying to write and talk at the same time. I'd definitely recommend checking out the app, I've found it very useful. Hope that helps!
@@AdamPanagos Which iPad will you recommend for creating such videos? Also, which screen recorder, mike you used?
@@nitindarkunde132 I just use my 2016 iPad pro. I just use the built in microphone and the Doceri app for recording.
thank u
How calculate eigen valued and vector 6 by 6 metric
The approach would still be the same; just the details would be more tedious since you'd be dealing with a much larger matrix. For larger matrices I would probably just use a computer/calculator to compute the answer unless you're required to show the details of your work. Hope that helps.
Adam
How do you get the final result at 4:26 from -8-8λ+4λ2+2λ+2λ2-λ3 ? Please Respond.Thanks
Edit:And also at 5:37 and 6:31 from the SET point downwards
All I'm doing is distributing the product (-4-L)*[-2-2L+L^2]. Just multiply it out.
thank you!!
You're welcome, thanks for watching.
why would you use the root formula on l^2 - 6l +8? that's much slower than just 8=(-2)(-4)...
Either way is totally fine, I just like sticking with the root formula to be consistent......
+Adam Panagos Thanks for replying. I would do the same if I'm a computer that never make mistakes. Sadly I'm not...
Me either....although I wish I was at times...=)
how can we write y=-z still confused :/
thank you
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.