Diagonalize 2x2 matrix

[@albertemc2stein290]

I'm a simple mathematician. I see a Peyam video. I like the video.

[@jacobpickos733]

The MAN, the MYTH, and the LEGEND. Thank you, Sir!!!

[@ServerDweller]

I've got my end of years exams coming up and I can't believe I've just found a single channel that covers such a large portion of the content. I wish I had found it sooner. Thanks for the video!

[@brianlamptey4823]

I've tried looking for this stuff online, this is the first time I've found someone who has cared to go into the 'how'.

[@jososa5717]

Clearest, best video on the topic. You have a gift for teaching, thank you so so much Dr. Peyam!

[@dolevgo8535]

MAN i literally had my linear algebra test two days ago :( damn it! anyways thank you so much!

[@Selenatorgirl544]

Thank you for being so positive in every video! (please don't feel pressure bc I say that.) It's so obvious that you love math and bc of this energy of you I feel like I can solve any problem :) Thank you again!!

[@drpeyam]

Thank you!!! 😁

[@eduardorivera508]

Ooohhh! I'm excited for the Legend Of Zelda analogy!!

[@yasseralg3928]

I love you! I said it to you first before my soon-to-be wife!!

[@drpeyam]

Awwwww, what an honor! 🥰

[@adelbennaceur7636]

thank you sir i really like your energy

[@BaljinderSingh-tf2sn]

amazing what a simple explanation to problem which looked very complicated!!!!!!!!!!! thanks alot !!!!! please keep uploading the videos you are doing amazing job!!!!!!!!!!!!!!! Great work

[@Titurel]

Dr. P is one of my math heroes!

[@determinantmatrix9584]

Really loved this video Thanks Dr. Peyam

[@MrCigarro50]

So great, as always, clear and helpful. Thank you.

[@unless14th]

Thank you for this solution. It makes me clearly and able to prepare teaching materials easily. Your explanation is easy to understand for many people who are interested in Math.

[@gvantsasakaruli9900]

You did something in such a short time that my professor has been struggling to explain for last two lectures with each being 1,5 hour long..

[@jacobvandijk6525]

What are you hiding behind that permanent smile? Uncertainty? A cruel parent? Naivety? Real happiness? Or what?

[@axollotl5813]

short simple and clear. Well Done 👍

[@jimnewton4534]

do you have an example video where you diagonalize a matrix with a 0 eigenvalue or with eigvenvalues of non-1 multiplicity?

[@noahalexander3607]

i love this man

[@mathkaveli11]

Love your work

[@nawelouahrani9588]

This guy is so cute, makes me want to learn more !!

[@raphaelcosta4352]

Tks, i love it. Linear algebra is very beatiful

[@adrianleranoz13]

Me encantan tus vídeos! Sigue así!

[@eliascaeiro5439]

42 ! Great video as always.

[@bradvincent2586]

wow this was insanely helpful!

[@dominikstepien2000]

That's great I've just started learning linear algebra, make more videos about LA, please!

[@drpeyam]

I have a whole linear algebra playlist if you’re interested!

[@dominikstepien2000]

Dr. Peyam's Show Thank you, I love your videos, keep up with great work!

[@azazahmed1842]

aahhhhh sooo helpful thaaanks

[@DrJessicaGrogan]

Are the signs on your null spaces for the Eigen vectors supposed to be switched?

[@DrJessicaGrogan]

Wait, seeing it doesn't matter because the difference is just scaling by -1

[@Contradi]

I don't know if the Legend of Zelda video you talked about is up, but does the analogy have to do with the Temple of Time in Ocarina? I won't spoil the analogy if that's it, but I have a hunch.

[@drpeyam]

Will be posted on Thursday 😜

[@Contradi]

Dr. Peyam's Show can't wait!

[@jeongohseo3631]

Thx for good lecture :) very helpful to me!!

[@brandonpanuco8546]

Thanks, im preparing to take my final.

[@drpeyam]

Good luck!!!

[@jesuisjustinian]

Just in time for my LA final today :D

[@eljonaballa6853]

My exam is tomorrow and here I am btw thank you for this video

[@plaustrarius]

eigenventors, meaning that the output vector of the transformation is in the same direction as the input vector. that's implied when you said the matrix minus (eigenvalue) x (identity matrix) is another matrix whose null space is non zero. what is my transformation rotates all of the inputs? this means your eigenvalues would be imaginary, with the eigenvectors having imaginary components themselves. Do hyper complex numbers show up for higher dimensional transformations? I would assume so, since you would need more distinct eigenvectors for transformations of higher dimensional space. I hate calling them imaginary numbers, this is such a natural development and use of them, its hardly imaginary at all.

[@lulinchuan5281]

such a pity not being able to meet u at berkeley！watch your video for both math110 and ee120(matrix exponential)

[@drpeyam]

I love 110

[@cicciobombo7496]

0:50 (A)li-A *TU TU TU TU TUM TUM TUM*

[@mohammedmadani7277]

I love dr peyam

[@nadeenyahya1384]

Thankyou well explained

[@akay37]

Thank you so much!

[@loveen3186]

great teacher

[@Gabbyreel]

Thanks!

[@nouralhuda3530]

Thank you

[@jessiemanopo]

What is the nul (matrix)?

[@tofu8676]

let A be a matrix then nul(A) (=nullspace of A or kernel of A) is the vectorspace of all vectors which multiplied with A would yield the nullvector. So if x is in nul(A) then Ax=0 (vectors)

[@Romulo_Cunha]

I'm sure you know it, but just one trick to help people find eigenvalues faster in this case, as you can notice the sum of columns is 3, which indicates one of the eigenvalues is 3, and the main diagonal tells us the sum of the eigenvalues is 7, so the other eigenvalue must be 5.

[@jagadishkumarmr531]

Wait, this works!! But how?

[@Romulo_Cunha]

@@jagadishkumarmr531by definition, Av=lambda*v. Assume you have a matrix which all entrances are a multiple of k. Then you can factor out the k so you will end up with a k*A which is exactly the definition of eigenvalues

[@holyshit922]

... but not always diagonalization is possible Maybe something about Jordan form ? Jordan form is generalization of diagonalization

[@drpeyam]

There’s a video about that :)

[@holyshit922]

If you presented Jordan form correctly viewers should not have problems with diagonalization but i dont thik that 23 minutes is enough to present all cases

[@Arycke]

Jacek Soplica Implying he didn't present it correctly. Both videos are simple to follow along with, albeit my main study is mathematics so I am quite biased. These videos aren't meant to be 100% comprehensive of everything except the individual problems or derivations of formulae. E.g. this and the Jordan form video serve to stimulate the viewer to delve deeper, to learn the basic methodology and terminology, and cover enough of the basics to get the viewer going in the correct direction. Also, one could try their own problem and find out that their matrix is defective and then investigate that as that is a lengthy subject to cover for beginners in a short video. The title is "How to Diagonalize," not "A Treatise on the Entirety of Matrix Diagonalization and Generalizations Thereof."

[@holyshit922]

I saw both his videos and videos from MIT and i think that videos from MIT are recorded better Jordan form was deleted from MIT but i still can compare other videos I had basics of analysis (functions, sequences,series, limits,single variable calculus ) on my high school I read on forums that they have deleted it lately from teaching program

[@Arycke]

Jacek Soplica Well you are entitled to think that. I don't know why you would speak of your freedom to compare videos here where it is practically irrelevant. What you said is akin to someone saying "Burger King nuggets are better" while stuffing their face with McDonald's chicken mcnuggets. Additionally, I and many others have had just as many ( or more) courses in high school than what you've described on top of their own personal endeavors. I don't see what that has to do with your original statement, so I'll write this off as a miscommunication due to a possible language and/or cultural difference. We all like mathematics and that's the most important thing my boi 💜 let's just keep it copacetic and watch any math stuff we want as we do and enjoy Dr. Peyam's enthusiasm and intelligence. Ya? :3

[@meh7272]

Like to dislike ratio is quite large as of now [210/0]. Its so large that we can't even comprehend it XD.

[@Myuri3146]

Do I have hope to get what that was promised... ?

[@drpeyam]

I’ve got videos lined up until mid-October, and that one is not one of them :/

[@Myuri3146]

Guess I will have to watch your video till mid-October then

[@omardelacruz9442]

nice

[@YorangeJuice]

i never liked doing diagonalization (especially orthogonal diagonalization), problems because they take soooooo long and are so tedious

[@douro20]

I haven't done anything with matrices in years...

[@avdrago7170]

When did you actually explain how to diagonalize a matrix?

[@drpeyam]

This whole process of finding eigenvalues/eigenvectors is called diagonalization

[@6612770]

I totally agree with AV Drago. This is the first session from Dr P. that I been left asking myself "Whaaaaaat?".

[@cameronspalding9792]

I thought the characteristic equation was det(A-lambda I)

[@drpeyam]

They’re the same since we’re setting it equal to 0

[@aneeshsrinivas892]

Here we go eigen

[@raichu56k]

if eigen do it, so can you !!!!!

[@ib9rt]

You didn't demonstrate that A = PDP^-1 at the end? More significantly, you didn't demonstrate why this procedure works. It's like doing math by rote, without understanding.

[@drpeyam]

That wasn’t the point of the video anyway!

[@halbmannhalbsib9881]

for intuition on the topic u can watch the videos done by 3b1b

[@nursultanbaitenov7505]

@@drpeyam you didnt solve P of -1

[@justwest]

1337 views and 123 likes, lol

[@cryptobeanbag7148]

Funny guy

[@Rundas69420]

What's the difference between an algebra-student and a trigonometry-student? Algebra one makes sign mistanes where the trig one makes sin mistakes. I'm going to bury myself for that one xD

[@AlessioAlessi]

You don't actually need to calculate that determinant for 2x2 matrices. You just need the matrix determinant and its trace and you can write down straightforward the characteristic polynomial 😌