Eigenvalue and Eigenvector Computations Example

[@JasonChuPoHan]

my lecturer explained this badly and you made me understand within 20 minutes!!! this helped me a lot!! thanks!!

[@maxchai6461]

for everyone that is having exam tomorrow, good luck! :D

[@ayushbhandari5017]

Today :)

[@draco_lich]

Thenx, mine was yesterday, but thenx anyway bud.

[@Ankurkumar14680]

Dear Adam, you have provided the best explanation to solve eigen vector....thanks a ton! God Bless You!

[@AdamPanagos]

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.

[@snackbob100]

fantastic video. No assumptions, ground up approach, that i greatly appreaciate. very clear. thank you

[@AdamPanagos]

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

[@vee_2412]

literally the most useful channel on the internet! thank you soooooooooooo much!!!!!!!!!!!!!!!!!!!!!

[@AdamPanagos]

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.

[@jonase2414]

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!

[@AdamPanagos]

Glad you found it useful, thanks for the nice feedback!

[@AdamPanagos]

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.

[@AliShan-yh2mt]

Watching at 1:30 AM.Test in the morning! You are a life saver !!

[@AdamPanagos]

Glad I could help and hope your test went well!

[@rsjosh7403]

Thank you so much, I finally understood how to get eigenvectors thanks to you!

[@AdamPanagos]

Great, glad to hear that. Thanks for watching!

[@HamzaAhmed-oq5od]

It's my exam tomorrow, thank you for saving me

[@AdamPanagos]

Glad I could help! I hope your exam went well!

[@khidrrr]

the ONLY problem with video was WHY WAS IT SO HARD TO FIND?! big THANK you! :)

[@desmond3092]

AaaaaDddxz

[@kasturivlogs]

This is the Best Video I found about eigenvalues and eigenvectors,You are a Great lecturer Mr Adam,Thanks for helping me :)

[@AdamPanagos]

Glad to help, thanks!

[@vishweshwarayyahiremath2527]

wow such an easy and brief methods he used to solve this problem. Loved his explanation and solving method. Thanks a lot sir

[@AdamPanagos]

You're welcome, thanks for watching!

[@hannukoistinen5329]

No you did't undersdand adytthin Vishmerayaahowdospeakvishnyshiva hireapartmentinhindi idiot!!!

[@ellenmalmin8375]

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.

[@klokklok3533]

Thank u big man. It's quite easy to just type eig(A) in matlab but would rather understand the concept behind it.

[@eriangelino7800]

You are the best teacher. Thanks a lot.

[@AdamPanagos]

Thanks!

[@AminaXXX3]

Saved my life with this video thank you!

[@AdamPanagos]

Glad I could help, thanks for watching!

[@rajp5307]

Sir, you made the things much simpler to understand..!😀Great job, sir👍👍

[@mkusasakala3861]

Wow that was FLAWLESS! thanks a lot

[@AdamPanagos]

Glad it helped, thanks for the nice feedback!

[@xbzq]

Actually, he messed up the last sentence.

[@MathScienceHistory]

You videos are always extremely helpful. Thank you!

[@AdamPanagos]

+Gabrielle Birkman You're welcome, thanks for the nice feedback!

[@terigopula]

You saved my exam.. Cheers :)

[@AdamPanagos]

Glad to help, hope the exam went well!

[@stevemalsnhu5096]

Adam, this video is pretty solid, nice job. (This is Steve Malbasa.) Thank you kindly.

[@icee562]

The scaling factor for the Eigen vector always confused me. Thanks for the clarifications!!!

[@justfortrollpeople8531]

thanks Adam you are the best teacher

[@brandoncazares8452]

Adam, this video's very helpful for me. Thanks.

[@AdamPanagos]

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

[@satyadutt8120]

Excellent that's called a perfect MATHEMATICIAN

[@thezmmc]

thank you so much Adam, you really helped me in my maths 2 college subject

[@AdamPanagos]

Awesome, glad I could help!

[@Faiselmoha]

I hope you are doing your MSc or phD now :)

[@willeett]

Thank you sooo much for the eigenvectors. I not seen the logic behind them at all. Thanks!

[@AdamPanagos]

Glad you found it useful, thanks!

[@willeett]

Gave me 4 points on the exam ;D (of tot 24)

[@bh4sh4]

This helped a ton thank you!

[@AdamPanagos]

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.

[@perdehurcu]

Selamlar. Çok güzel bir ders olmuş. Tama aradığım dersti. Ağzınıza sağlık. Teşekkürler.

[@fatimahbawazeer8974]

Thank you very much , helped me so much this semester

[@MM-mc9ne]

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 .

[@hannukoistinen5329]

Thanks mään, shut your mouth mään!! And don't smile!!! Thänks mään!!!

[@Mike-tu4lc]

easy to understand, thanks sir

[@AdamPanagos]

You're very welcome, thanks for watching.

[@clintonkas3508]

I instantly got lots when your started the eigen vector

[@lowhaoming4238]

in 5:15 ,isnt that the formula of finding determinant is 1-2+3 ? Please reply thanks!

[@AdamPanagos]

I already included the negative sign with the 2 term when I did that initial calculation. So, it's just the sum of all the parts. Hope that helps. Adam

[@computology]

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?

[@AdamPanagos]

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

[@aminaattar833]

thank you so much for your help

[@AdamPanagos]

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.

[@SuperLuckyKill]

I really liked this presentation.

[@err3088]

Thanks! And I really like your font!

[@AdamPanagos]

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

[@elleoliveira5316]

Excellent. Do you give online private classes?

[@AdamPanagos]

No, at the moment I don't. Never really though it about it honestly......

[@charlesamofordjuoh9940]

thanks man you helped me so much this semester

[@AdamPanagos]

+Charles Amofordjuoh Excellent, glad to hear that. Thanks!

[@tlt2237]

Clear and efficient presentation! Thanks!

[@AdamPanagos]

+tlt You're welcome, thanks for watching!

[@MichaelRhodess]

wtf youre actually so lit at explaining everything

[@AdamPanagos]

Thanks much, glad I could help!

[@ADR-f9u]

thanks for the video!! it is really helpful. I just wanted to understand how at 6:25 you arrive at lambda1 = 0? Why is it so obvious? Because the RHS = 0, this lambda has to be 0 (o times anything = 0?)? If so, since the RHS is always 0, why then not all lambda1 = 0?

[@executorarktanis2323]

4 years damn

[@mailmayankpandey84]

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.

[@prithvirajpodder1502]

Sir, but how do i calculate the eigen values if there is also a constant in the equation(with the lamda values as well)?

[@AdamPanagos]

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.

[@prithvirajpodder1502]

Thank you :)

[@doaard9174]

You made it easy like 1+1

[@burkee3086]

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

[@AdamPanagos]

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.

[@yakkaliharshitha6006]

Great explanation sir

[@hamzaaead9680]

بارك الله فيك رائع ما شاء الله

[@AdamPanagos]

Thanks for the kind words, thanks for watching. Best, Adam

[@JashanTaggar]

What a beautiful video!

[@AdamPanagos]

Thanks! Make sure to check out my website adampanagos.org for additional content you might find helpful. Thanks again, Adam.

[@samitpaudel7886]

Thank you very much sir.

[@harrsheethas6827]

that helped me a lot! thank u so very much!

[@gavinmaboya1]

this is an excellent video. do you not have anything on the Gram-Schmidt algorithm?

[@AdamPanagos]

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.

[@haseebsedeqi5351]

wonderful finally i got it thanks a lot!!

[@ck3908]

good example.

[@dinovdesignco]

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

[@AdamPanagos]

All I'm doing is distributing the product (-4-L)*[-2-2L+L^2]. Just multiply it out.

[@activeman1816]

very easy to understand sir ,thank u so much.

[@yens086]

thank you for this video please in 6:00 i dnt understand how you took the like terms please i need your reply as soon as possible i have exam in two daYS TIME

[@AdamPanagos]

To find the eigenvalues we need to solve for the lambda such that det(A-LI) = 0. The first part of the video is working through what det(A-LI) is. This computation was broken down into three parts. After computing all three parts we have det(A-LI) = part1 + part2 + part3. Since we want to know when this is equal to zero, I set this quantity equal to zero, i.e. det(A-LI) = 0. This equation is a function of lambda. We find all values of lambda that satisfy the equation. These are the eigenvalues. Hope that helps.

[@yens086]

Adam Panagos oh thank you sir i got it now God bless you sir

[@senthilsiddhu2]

thankz for the clear picture.....

[@k.m.1851]

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?

[@aliameli3757]

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.

[@AdamPanagos]

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!

[@natetung4219]

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

[@thr_btsfanx6832]

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.

[@AdamPanagos]

+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.

[@alameeryamen1045]

Very good man 💜

[@AdamPanagos]

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.

[@akhil5g199]

it's really good...!! I just got an easy way to solve the problem

[@lynns4122]

Thank you!

[@AdamPanagos]

You're welcome, thanks for watching!

[@mercyjepchirchir266]

thanks alot for the help in eiglen values and vectors be blessed

[@jt0851]

Thank you this helped me alot.

[@alphalimit8]

Hello Mr. Adam can you make a tutorial for jordan form representations in matrix 2x2 or 3x3? :) Thanks.

[@tonymurphy6952]

awesome stuff, have you got more tutorials??

[@AdamPanagos]

Glad you liked the video. If you're looking for more I have about 170 or so videos on my KZbin page (kzbin.info) 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.

[@muhmazabd]

Awesome, Please how did you create this video???.... Which software please

[@AdamPanagos]

Glad you liked. I use an app on my iPad called Doceri, you can get it at doceri.com/. Very nice for making videos such as this. Hope that helps.

[@sydl2799]

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

[@AdamPanagos]

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.

[@bergrahm]

I have a question regarding the third eigen-vector. When I do this, I chose not to choose, as you did, z=3 and got (-1 -5 1)^t how did you know that 'selecting' 3 for z would be the correct answer.I got the other ones using the exact same steps but having z = 1, so I do not think the method is wrong, just confusing last step.Otherwise 10/10 this has helped me so much!

[@AdamPanagos]

+Axel Bergrahm Glad the video helped! With respect to your question, the choice for z is completely arbitrary. The final answer for the 3rd eigenvector must have the form [-z; (-5/3)z; z]. This is a valid eigenvector for any value of z. Note that as we change our selection for z, the final vector changes, but he DIRECTION of the vector is always the same. So, another valid choice would be z = 6, which would result in the eigenvector [-6; -10; 6]. Note that this vector is just twice the one I used in the video, but still in the exact same direction. Since the choice for z is arbitrary, there are an infinite number of other valid choices as well. You may want to check the answer of [-1; 5; 1] that you noted. This doesn't appear to match the general form for any value of z that I can figure out. Hope that helps and thanks for watching! Adam

[@bergrahm]

thanks for the great answer! And I'm really sorry for my late reply, this clears things up completely, also I figured out how I was approaching the problem incorrectly. I want to thank you for your great video again and also for answering questions that we have. Big fan!

[@AdamPanagos]

+Axel Bergrahm Glad that cleared everything up for you, thanks for watching!

[@WAB1980]

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...

[@AdamPanagos]

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!

[@nitindarkunde132]

@@AdamPanagos Which iPad will you recommend for creating such videos? Also, which screen recorder, mike you used?

[@AdamPanagos]

@@nitindarkunde132 I just use my 2016 iPad pro. I just use the built in microphone and the Doceri app for recording.

[@XiaosChannel]

why would you use the root formula on l^2 - 6l +8? that's much slower than just 8=(-2)(-4)...

[@AdamPanagos]

Either way is totally fine, I just like sticking with the root formula to be consistent......

[@XiaosChannel]

+Adam Panagos Thanks for replying. I would do the same if I'm a computer that never make mistakes. Sadly I'm not...

[@AdamPanagos]

Me either....although I wish I was at times...=)

[@elysegroenewegen4599]

how do u know which eigenvalue is 1, 2 or 3

[@abhishekdasgupta4786]

Use the formula -b+or-√(b^2-4*a*c)/2*a to compute the roots of the equation

[@madenaarcher9051]

BIG THANK YOU

[@vividflair-mw4xp]

Very helpful.. thanks alot

[@AdamPanagos]

You're welcome, thanks for watching!

[@modelaircraft12]

fantastic! thank you a lot Sir!

[@AdamPanagos]

+franco diaz You're welcome, glad you liked!

[@hazzel858]

great work!!

[@ahmadalarnous2787]

you are the besttttttttttttttttttttttt

[@AdamPanagos]

Thanks!

[@sewanuprety3626]

Life saver!!

[@AdamPanagos]

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

[@shubhampawade2933]

That was smooth.

[@abidmalik3160]

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 ?

[@samimahassan1716]

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

[@AdamPanagos]

Good luck! Hope your exam went well!

[@deepakrana-nu9xp]

sir please answer me this after getting the final equation you changed the signs of the equation in the eigen values why????????????????????????????????????????????????????????????

[@sf2265]

what would happen if in the final equation (1)+(2)+(3) instead of +0 would be positive number?

[@AdamPanagos]

+Egor Baranov We're solving the equation det(A-LI) = 0 to solve for the eigenvalues. The left side of this equation is the what I broke down into the parts (1), (2), and (3). If you solve for this equation equal to something other than zero, then you're not solving for the eigenvalues of the matrix. The right side has to be zero. You still COULD solve for this equation equaling something other than zero, but I don't know what the solutions of this equation would mean. Hope that helps, thanks for watching! Adam

[@tirbehofficial3387]

Am here 8 years later💪

[@AdamPanagos]

Eigenvalues and eigenvectors are timeless......

[@nuwanatthanayake]

Great Sir.

[@AdamPanagos]

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

[@joelkaleshi5280]

easy to understand. thanks

[@abhinetrakumar]

very nice explanation. thank u.

[@jianweiyeow9715]

how did u know [-12 -20 12] when checking the answer??

[@AdamPanagos]

Since v = [-3; -5; 3] is an eigenvector of A, by definition we know that Av = Lv where L is the eigenvalue associated with eigenvector v. We can compute Av to get [-12; -20; 12] by just performing a matrix-vector multiplication of A with the vector v. Hope that helps, Adam

[@tevitaclarke7499]

Really good stuff.

[@AdamPanagos]

Thanks!

[@samfitzpatrick1866]

What if when I reduce the nullspace I get the vector [100, 010, 001] instead of [100,010,000]?

[@AdamPanagos]

***** It's actually impossible for that to happen. Since eigenvectors are the null space of the given equation, you MUST end up with a row of zeros. Hope that helps!

[@samfitzpatrick1866]

Thankyou for the reply and i understand what you're saying but can't figure out this exam question then because whenever I reduce i dont get a row of zeros. 5 −4 −4 2 −1 0 0 0 −1 Here is the initial matrix, if you wouldn't mind as too helping me and seeing if it can be reduced with a row of zeros. Thankyou

[@manasrath773]

dis video make my day... thanku a lot sir... :)

[@AdamPanagos]

+manas rath Glad you liked it, thanks!

[@ANUJ509]

Gr8 video n explanation too

[@samindakularathne]

Thanks a lot :) Its surely gonna be useful

[@AdamPanagos]

Glad you liked it, thanks.

[@bilalon]

great job Man thank you so much