Find Eigenvalues and Eigenvectors of a 2x2 Matrix
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- Опубліковано 22 лют 2016
- We work through two methods of finding the characteristic equation for λ, then use this to find two eigenvalues. We use Ax=λx to calculate two eigenvectors, then look at a visualisation.
Thanks for explaining "eigen" things with what has to be the *clearest* and *fewest* words possible in both this and the next video about diagonalizing. I say that after watching a dozen other videos on this topic, including some with elaborate moving graphics and animated icons. Most needlessly confuse exposition of concepts for exposition of methods, which you have skillfully avoided. Thanks again.
Many thanks!
Absolutely love your method of teaching! Your pace and showing by examples is what makes you stand out amongst other tutorials on UA-cam. Thank you.
Thank you so much for your wonderful feedback!
This is the clearest explanation of Eigenvalues and Eigenvectors that I've seen. Showing the transformations on the graphs ties it all together. Thank you!
@G Hamilton: Thank you so much for this feedback - much appreciated!
A very clear explanation of the subject. Probably one of the clearest ones I've seen. Well done......
@John: Thank you very much!
Thank you so much for all the effort & time you put into explaining all of this so clearly. Gonna learn a lot from your other videos as well. THANK YOU!
@Paras Sharma: That's very kind of you...thank you!!
This series was one of the clearest and best ever. Thanks very much.
Thank you!
I don't know a thing about eigenvalues and eigenvectors and i am trying to learn and this is the best and easiest video i could find on this subject. I am glad it only had 1 example so i can re-watch this video as many times as i need to without feeling overwhelmed or confused or frustrated👍👍
@adorable wiggling bunny nose sugar high: Thank you so much!
@@MathsWithJay Your very welcome!😀😀
This is like the 6th video I have watched; I finally understand it (kind of). Thanks!
Glad it helped! If you're still unsure....do you have a question?
Thanks this was the best video that clearly explains the terms. Keep it up. You are doing a great job.
Thank you so much!
You've made this concept to be so easy and clear in a short time....thank you very much
@Pauline Dametula: You're very welcome!
Your videos are by far the best to explain Maths procedures ! No matter how many steps are involved, your explanation is clear and concise. (Level 2 OU student here!)
Thank you ♥️
Glad you like them, Sheema...I tutor on level 1 OU modules, and started this channel after making some of the screencasts for MST124.
@@MathsWithJay I thought your voice was familiar and had read on one of your other videos that you were an OU tutor 😄
@@MathsWithJay how do u get 2x-y = 0
At what time in the video?
THANK YOU SO MUCH
You don't understand how much you've helped me. Thank you.
You are so welcome!
this has to be the best video on this topic, thank you.
@Hamza Haruna: Wow, thank you!
Finally, I found a woman who explains maths at the level I am studying. Thankyou
Happy to help!
Thank you for making this video. It helped me alot in my Vector Class :)
@Adriel That's great! Thank you for letting us know.
Very clear explanation, in the sweetest voice, thanks a lot.
You are most welcome!
Thank you so much for your videos! It helped me a lot!
Thank you!
I wish you I found you at the beginning of my semester. Thank you.
@Sayem: Thank you!
@@MathsWithJay ♥️
very clear since you have explained why det(A - lmda * I) = 0, everything makes sense, many thanks!
You're very welcome.... Thank you for your useful feedback.
great lecture, thank you!
Many thanks for your super feedback.
Very helpful,thanks!!
Many thanks for the great feedback.
Very well explained. Thank you.
Glad it was helpful!
very nice explanation...thanks a lot.
can u upload lectures of complex variables including Taylors theorem and all.
If the characteristic eq have complex roots then who we can find the eigenvectors
many thanks,i need a lecture about participation factor
I'm going through this and I can't be more confused. I managed to do the eigenvectors but all sources anywhere shows that you can basically place the ratio in any way, shape and form possible as long as the numbers are correct, even my textbook and an online vector calculator contradicts each other where for x=-y, you get [1:-1] from the book with [x:y] = [x:-x] = [1:-1] as it's logic, and [-1:1] from the calculator with [x:y] = [-y:y] = [-1:1]. And that's where I'm completely stuck as later parts that concerns differentials will produce drastically different answers if the modal matrix is different, which the modal matrix largely depends on how you present the eigenvectors which you can present it however way you like to.
Would you mind to explain how is this possible and how can I use the right P matrix for further work? and how do you decide that lamda1 is -1 and lamda2 is 8, since the quadratic equation does not produce numbers in specific orders.
It doesn't matter which way round you choose lamda1 & lamda2, but this will affect the P. Have you seen the other relevant videos in ua-cam.com/play/PLgQUIweMg9eJP1QeCotIspOmwGUd8jibS.html ?
Many thanks. Your video is very helpful. Is there a formula for finding the characteristic equation of a 3x3 matrix and possibly a 4x4 matrix like the one we have for a 2x2 matrix? kindly help me with it if it exist.
Thank you, John. Have you seen ua-cam.com/video/j2B_vcp3tUQ/v-deo.html ?
can u give lecture normal form and canonial form matrixes?
hi amazing vid quick question does it matter which lambda is which as I made my lambda 1 (8) and my lambda 2 (-1). because this does affect the eigenvector matrix u where you combine the left and right side.
It doesn't matter which you chose as lamda 1 and lamda 2..Thanks for your feedback
Thank you very much!
Thank you!
THANK YOU VERY MUCH!
Thank you!
Good lesson!
Thank you for your feedback; it's good to know that you are finding our screencasts useful.
Wow beautiful explanations thank you ♥️
You’re welcome 😊
Thank you so much!
@Elie: Thank you!
helpful, thank you
Thank you!
Thank u for clarification
You're welcome 😊
very nice keep it up thanks
Will do, thank you.
Hi, why do you need to use the identity matrix in order to take the x outside the brackets?
@Leo: So that each term in the equation is a matrix
super helpful
:)
What a legend :0
@Jose: Thank you!
How would it work for lambda ^2 - 2 (lambda) - 15 = 0? ????? PLEASE HELP.
You are looking for two integers that multiply to 15 and have a difference of 2. See ua-cam.com/video/sMj1GAc3hAU/v-deo.html for examples of factorising quadratics.
very helpfull thanks
You're welcome!
on 14.03, y=-x, therefore the eigenvector is [1 -1]. May I know if the eigenvector could be [-1 1] also coz I put x=-y?
I show AN eigenvector. Any multiple works too...your values are -1 times mine, so this works too. Note that you can check your eigenvector as I did with mine.
Noted. Thank you very much
Thank you, this was clearing up everything I didn't understand about Eigenvalues and Eigenvectors... I have gone through lots of material trying to figure out what is was about and finally managed to understand this now ... thanks again.
You're very welcome! Thank you for taking the time to give such detailed feedback - it is appreciated.
Thanks dia well understood
ty
The best.
Thank you!
At 12:30 can the eigen vector be (-1,1) since x +y = 0 is the same as x= -y?
Yes...there are an infinite number of eigenvectors that satisfy x + y = 0
Thanks for taking away my worry
No problem
VERY GOOD
Thanks so much for your excellent comment
Tq soo muchh💓
@SUZZ Official: Thank you!
Should I be assuming the value of x as only 1 or can it be any value? I have an equation y+2z=0, and I rearranged it to y=-2z and assumed y as 1, the eigenvector came out as (1,-0.5). It does not match the solution in the book I am following. The solution is (2,-1)
@Rahul: When you find an eigenvector, the ratio is important. Doubling your numbers gives "the solution", so it looks like you are correct too.
Maths with Jay I tried checking it, and it works, thank you
Excellent....thank you for letting us know.
Very simple and clear explanation thank you
@LADYBEE bunge: Thank you!
is formula to find characteristic equation of 3*3 matrix?
It's simpler to do as shown here: ua-cam.com/video/j2B_vcp3tUQ/v-deo.html
Hi Jay, I've been applying the methodology to the rotation matrix:
(0 - 1)(x) =(0)
(1 0)(y) (0)
Has eigenvalues, è =+/- 1.
I can't seem to get sensible values for the eigenvector when è=1:
-1x - 1y =0
1x - 1y =0
or when è=-1:
1x - 1y =0
1x +1y =0
... Basically x=y and x=-y
Can you help?! 😬
Peter
The eigenvalues are i and -i...I can't understand what you've written for your eigenvalues - I'm seeing an e with an accent on it.
@@MathsWithJay you're right the eigen values are +/-i. Does this mean that there cannot be any real eigenvalues in the 2D this 2D system . I wonder what would happen in the case of the rotation matrix in 3D with rotation purely about the z axis.
I got the 2nd Eigen vector -1 and 1
And it also satisfies the equation But I am confused which one is correct mine or yours 😢
They are both correct. Note that I have written "an" eigenvector, so any multiple of my answer is correct.
I have exam in three hours about this topic , let's goooo!!!
Hope it went well!
@@MathsWithJay it went very well , we had question about this topic , and I did it easily thanks to your video!expecting my grade to be between 75 - 100 thanks again👍🏻🙌
in 9:33 why the eigenvector is 1 and 2? i dont understand.. can u explain more, please? anyway thankyou for sharing this video
The important point is the relationship between x and y. You can choose ANY value for x, but then the y value is double the x value. x=1 is one of the simplest values to choose, but you could choose another value....what would y be if you choose to take x = 5?
i understand, no need explanation, thx
Class is very nice. But sound is not audible. Please increase a little. Thanks
Thank you for your feedback
I think you are switching the values of x and y!
@abbas sab: At what time in the video?
So who wants to calculate what happens to the point (5,4) like she suggested towards the end of this video? Anyone?
@adorable wiggling bunny nose sugar high: Why not try it yourself?
@@MathsWithJay i don't know what equation the point (5,4) is supposed to go into.
Write down matrix A, then (5, 4) as a column vector, then multiply the matrix by the vector. The answer will be a column vector...you can then write this as the coordinates of a point. What point do you get?
@@MathsWithJay Oh i thought i just put the point (5,4) in one of the y= equations. See i told you i didn't know what to do!😂😂😂😂😂😂
@@MathsWithJay i am still trying to figure out what point i get in this problem from solving it.
On 9:40 can the answer also be [1/2 1]? [6 -3 0 0] / 6 => [1 -1/2 0 0] => x1 = 1/2 x2 , let x2 be 1 and x1 will equal 1/2?
+calc hacks There are an infinite number of eigenvectors for each eigenvalue. To check if your solution works, just multiply it by the matrix and the eigenvalue - if they give the same answer, you know you have a correct eigenvector.
Where it came from the 2x-y=0
At what time in the video?
8:54 sir.
Where does 2x-y=0 came from?
@@MathsWithJay i can't eigher understand where it came from. at 8:54 in the video. how 6x-3y=0 can be 2x-y=0? i my head it's should be: 3 ( 2x-y) = 0 ?
Yes, then divide both sides by 3
@@MathsWithJay what math rule is that? Or do you where I can find more information about that? What is it called in English? Thank you so much in advance:)
😁😁😁🙏
ty
very good video but I had to replay the video many times because there weren't any subtitles, and it's quite hard to catch up with your British accent, can you please add subtitles ? 🙏
Thank you for your feedback. Most of our recent videos have subtitles. Does it help to slow down the speed of the video?
@@MathsWithJay a bit but thankyou for responding
Anyone knows why -3 × -6 = -18???
@Sam: unlikely!!!
because she was doing the determinant theres a negative sign there, det(2x2 matrix)= ad - bc
+18
there is something wrong lamda1 =1, lamda2= -8.
Your answers are wrong...so watch the video to find the correct answers and to see how to check them.
Well Done, you started with (A -lamda I)x =0 and unknown lambda & x . Most start with knowning either lambda or x.
For example Introduction to Eigenvalues and Eigenvectors - Part 1 ua-cam.com/video/G4N8vJpf7hM/v-deo.html
This was helpful...but i still understand why the volume was sooo low...that wasnt cool
Yaäh the volume oops very low but it a nice explanation
your wrong
At what time in the video?
Why is it always the simplest ones lmao, why are these same equations when you put a specifi eigen value, if you are that lazy to do with different ones, do not do it at all.
At what time in the video?