Eigenvalue and Eigenvector Computations Example
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- Опубликовано: 7 сен 2024
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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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my lecturer explained this badly and you made me understand within 20 minutes!!!
this helped me a lot!! thanks!!
for everyone that is having exam tomorrow, good luck! :D
Today :)
Thenx, mine was yesterday, but thenx anyway bud.
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
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
It's my exam tomorrow, thank you for saving me
Glad I could help! I hope your exam went well!
Thank u big man. It's quite easy to just type eig(A) in matlab but would rather understand the concept behind it.
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.
Thank you so much, I finally understood how to get eigenvectors thanks to you!
Great, glad to hear that. Thanks for watching!
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!
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!!!
You are the best teacher. Thanks a lot.
Thanks!
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.
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.
Sir, you made the things much simpler to understand..!😀Great job, sir👍👍
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!
Saved my life with this video thank you!
Glad I could help, thanks for watching!
Wow that was FLAWLESS! thanks a lot
Glad it helped, thanks for the nice feedback!
Actually, he messed up the last sentence.
Watching at 1:30 AM.Test in the morning! You are a life saver !!
Glad I could help and hope your test went well!
You videos are always extremely helpful. Thank you!
+Gabrielle Birkman You're welcome, thanks for the nice feedback!
The scaling factor for the Eigen vector always confused me. Thanks for the clarifications!!!
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!
Selamlar. Çok güzel bir ders olmuş. Tama aradığım dersti. Ağzınıza sağlık. Teşekkürler.
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.
thanks Adam you are the best teacher
Thank you very much , helped me so much this semester
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)
I instantly got lots when your started the eigen vector
I really liked this presentation.
Excellent that's called a perfect MATHEMATICIAN
Thank you very much sir.
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!
wtf youre actually so lit at explaining everything
Thanks much, glad I could help!
thankz for the
clear picture.....
thanks man you helped me so much this semester
+Charles Amofordjuoh Excellent, glad to hear that. Thanks!
Thank you!
You're welcome, thanks for watching!
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.
Great explanation sir
it's really good...!! I just got an easy way to solve the problem
Clear and efficient presentation! Thanks!
+tlt You're welcome, thanks for watching!
wonderful finally i got it
thanks a lot!!
easy to understand, thanks sir
You're very welcome, thanks for watching.
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
good example.
بارك الله فيك رائع ما شاء الله
Thanks for the kind words, thanks for watching. Best,
Adam
thanks alot for the help in eiglen values and vectors be blessed
that helped me a lot! thank u so very much!
You made it easy like 1+1
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.
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.
What a beautiful video!
Thanks! Make sure to check out my website adampanagos.org for additional content you might find helpful. Thanks again, Adam.
very easy to understand sir ,thank u so much.
Thank you this helped me alot.
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!!!
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.
Very helpful.. thanks alot
You're welcome, thanks for watching!
fantastic!
thank you a lot Sir!
+franco diaz You're welcome, glad you liked!
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
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.
Thanks a lot :) Its surely gonna be useful
Glad you liked it, thanks.
Easyly understanding it is better
Thanks!
Life saver!!
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
BIG THANK YOU
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 :)
Excellent. Do you give online private classes?
No, at the moment I don't. Never really though it about it honestly......
Thanks
You're welcome, thanks for watching.
easy to understand. thanks
very nice explanation.
thank u.
Thanks very much
you are the besttttttttttttttttttttttt
Thanks!
Thank you
dis video make my day... thanku a lot sir... :)
+manas rath Glad you liked it, thanks!
That was smooth.
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
Really good stuff.
Thanks!
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...=)
thank you!!
You're welcome, thanks for watching.
Gr8 video n explanation too
Hello Mr. Adam
can you make a tutorial for jordan form representations in matrix 2x2 or 3x3? :) Thanks.
great job Man thank you so much
Perfect!
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
great work!!
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?
Good
Thank you so much
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.
Which software u used to teach
For most of my videos, I use Doceri (an app for my iPad) that lets me pre-record all the writing. Then, I can "play back" the writing while I record the audio. Hope that helps,
Adam
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.really helpful
Am here 8 years later💪
Eigenvalues and eigenvectors are timeless......
super !!!
Green highlight ❤️
how do u know which eigenvalue is 1, 2 or 3
Presentation ❤️
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.
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!