Diagonalize 3x3 matrix

[@Peter_1986]

His enthusiasm makes this feel like an exciting adventure.

[@hihiirokane_gbf]

adorable teacher, effectively learning, Thank you!!

[@drpeyam]

You’re welcome! 😄

[@MrRyanroberson1]

In soviet russia 14:12, equation long-divides you.

[@tinyasira6132]

He is such a happyyyy man!!! 😂😂 I wish I could be this much happy too while doing linear maths! 🤣

[@bakeurstew1434]

This madman is doing it all by hand

[@ralfschmelcher9673]

This is a great explanation, thank you!

[@mahreenathar6928]

Isn't it supposed to be 4 in the first column instead of -4?

[@TheROSIEPEPPER]

I love this guy's energy

[@liakondova4341]

love your attitude!!

[@shokan7178]

"Heeeeey, but it's so much easier to factor out (lambda+1) here and (lambda+1) here!" (3:34)

[@Furiac.]

love your enthusiasm about lin algebra

[@aaron_mg00]

Wow thank you, you made me understand how to do this, you explained it very well, but i didn't understand at all how you did the determinant, anyway i tried it using other method and i got the same solutions!! Thank you very much Greetings from Spain!!

[@vitalsbat2310]

For a more generalized case of cubic: You should use make the function into a depressed cubic, then solve it by comparing the depressed cubic with the identity (m+n)^3, then jump into the complex world that gives you some sort of cube root of a complex function, and you one of the solutions, the other solutions could be found with long division. But if you do this then this video will be like 10 hours

[@dominicellis1867]

If you set lambda to 10, you can use number theory to perform a prime factorization. In special cases, this will lead to a factorization of lambda when converted back into a variable. A prime example of this is x^2+2x+1. This converts to 121 which factors as 11^2. 11 = x+1. For certain factors of P a*10 + b might not convert easily back to ax+b because while 5*6 = 3*10, (x-5)(x-4) \= (x-7)(x). I’d be interested in a video on the conditions where the factor ax+b = a*10+b.

[@samg8832]

Thank you very much. You are very effective and cool teacher.

[@deborahodion4794]

Good tutorial on diagonalization. Thank you

[@wes9627]

If you normalize each eigenvector to unity, the matrix P will be orthonormal and its inverse will equal its transpose. So no work beyond normalizing the eigenvectors is required to get P inverse.

[@nullplan01]

The RRT is fairly easy to prove: Let f(x) be a polynomial of nth degree with integer coefficients. Assume p/q is a rational root of that polynomial. Then f(p/q) = 0. If you multiply that equation by q^n, all terms on the left hand side will be integers. Of these, the leading term a_n p^n has the distinction of being the only term that is not a multiple q. So we can subtract it, then bracket out q on the left hand side, and we get that -a_n p^n = q(some integer). Since p and q are coprime, the only way that equation can hold is if a_n divides q. That's why the denominator must be a divisor of the leading coefficient. Returning to our equation f(p/q) * q^n = 0, we see that what is left of the constant term a_0 q^n is the only term that is not a multiple of p. Analogous to the above, it follows that p must be a divisor of a_0, so the numerator must be divisor of the constant part.

[@AG-xlr]

You have a strong positive vibe💪

[@MazenFiki]

my best reagrades and respect from egypt

[@jerrychan4052]

he is super excited. great video.

[@jeremyb1346]

Tant qu'on y est, on aurait même pu calculer l'inverse de A en utilisant le théorème d'Hamilton-Cayley ^^ J'ai hâte de voir la suite ! : ) On a un peu de trigonalisation de prévu ?

[@buttersalad117]

that sign mistake solution was nice.

[@musicismyIife]

it is so useful for me!! i wish you were my professor

[@drpeyam]

❤️

[@Rundas69420]

But I thought that the rational roots theorem says, that if you're taking an exam, all roots of a cubic polynomial are integers between -3 and 3. And also there is one brutal formula that directly calculates the characteristic polynomial p(x). p(x)=x^3-trace(A)*x^2+(det(A1)+det(A2)+det(A3))*x-det(A). Ai is the minor of A which is acquired by bomberman-ing the i-th row and column.

[@ytsimontng]

Nice exercise! I calculated P-1 to be [0 -1 1,1 2 -1, -1 -1 1] in your columnorder where the commas seperate the rows. Thanks

[@AttiyaAnwarAhmed]

Hello i really enjoyed the video but i have a doubt if an eigenvalue has 2 basis what will be the P matrix then ?

[@jiusandrokuhn8023]

Congratulations for the work. The matrix of the video cover is wrong. I tried to solve without looking at the solution and came up with a complex solution.

[@cusackprep]

Why not factor by grouping at 6:30?

[@nawelouahrani9588]

Thank you so much for your videos ! Very clear and good energy 😊😀

[@motherisape]

came to learn about digonilization of matrix learned amazing fact about polynomial

[@peterhunt1968]

The row reduction method seemed to me longer than simply multiplying out the vector (x, mx + c ) and then quickly solving 3 simultaneous equations. You still end up at the same place don’t you?

[@drpeyam]

Never heard of this other method :)

[@MonkoGames]

my teacher wants it for a 3x6 matrix where all the values are in the couple thousand except for 1 zero and im dying

[@drpeyam]

Omg I’m so sorry! Also 3x6 is not possible, do you mean 6x6?

[@MonkoGames]

@@drpeyam Here was the question: Let A be the 3 × 6 matrix given below: Find invertible matrices P and Q such that P AQ is a diagonal matrix with only 1s and 0s along the diagonal. I said there was no solution since invertible matrices have to be square, which wouldn't produce a square output.

[@TheMauror22]

What is the condition for a matrix to be diagonalizable?

[@Debg91]

I don't know about necessary conditions for the general case, but there are some important sufficient conditions: if the matrix is symmetric or Hermitian, it's always diagonalizable

[@drpeyam]

Basically enough eigenvectors :)

[@TheMauror22]

Is the diagonal matrix unique for the other matrix?

[@war_reimon8343]

Determinant non-zero

[@Idtelos]

When you see 3x3 matrix, you are hoping for Symmetric positive definite. Makes things so much easier...lol.

[@drpeyam]

Definitely LOL

[@rodrigogimenez8385]

You could use Ruffini's Rule for that polynomial division?

[@drpeyam]

What’s that?

[@drpeyam]

Sounds like Fubini, haha

[@aryanjain9957]

@@drpeyam Its basically synthetic division

[@rodrigogimenez8385]

@@drpeyam en.m.wikipedia.org/wiki/Ruffini%27s_rule

[@rodrigogimenez8385]

@@drpeyam it's very useful. We learn it at high school as an easy way to probe some number is root of a polynomial

[@마도로스J-f4o]

Thanks for the video

[@drpeyam]

Welcome :)

[@peterhunt1968]

Thank you. Great video.

[@PonyExpressOSRS]

Why divide by lambda - 1 during long division?

[@drpeyam]

It’s because 1 is a root, so lambda-1 is a factor and hence we can divide by it

[@Titurel]

@@drpeyam thanks for clearing that up. I was a little confused too.

[@manizabayovedaste5142]

Thank you very much lecture if possible you may explain for Me more and many exercises and I need to attend this class

[@tusha6988]

Thank u sir...♥️

[@colloupdated]

u are welcomed

[@gvantsasakaruli9900]

So this is basically using Horner's method to find the Lambdas

[@jokerfunny1146]

It is a great explanation but you made it complexly no need for all that ,teacher

[@54.5mviews3]

Great Work

[@theechocolatpapii4052]

great vid👌

[@mimithewienerdog6928]

Great video!!! FYI The thumbnail matrix does not match the video matrix. There's a 3 in the thumbnail where there is a 4 in the video.

[@drpeyam]

Haha, clickbait 😂😂😂 But thanks, I’ll fix it

[@mimithewienerdog6928]

@@drpeyamHaha! Thanks!

[@xavy_921]

Thank u sir ❤️

[@Cupekacke]

how did lamda times - 3 equal a -4lamda ?????

[@hellheaven4167]

Show the time so we can find the issue

[@pedrososa2460]

If a matrix is diagonizable then it has eigenvalues?

[@drpeyam]

Yeah

[@LuisBorja1981]

How about synthetic division showing only coefficients?

[@drpeyam]

I think that works, I’ve never learned synthetic division, actually

[@sunnyjung2980]

you look really happy lol

[@sergejavdic]

Is this really so much fun for you my man?

[@drpeyam]

Yes it is!

[@abhishekmazumdar2072]

Amazing

[@debalinanag8140]

Thank you very much sir

[@christiankorkies7822]

Thanks sir

[@FFernandezB]

Hello! I like a lot your videos and I would like know if you can make a video of triangulization with T-conductors, minimal polinomial, etc Thanks a lot for too much math

[@surajvarne3992]

god bless you

[@Xnibblet]

I start laughing you when you are excited about finishing. I thought the finding the eigenvalue followed the formula A-λI and not reverse, or does it matter?

[@drpeyam]

Doesn’t matter, since we’re setting it to 0

[@brolien3717]

10:54

[@mosheramakuri7039]

Can you speak some what slow it understands better resy of all it was awesome thankyou so much

[@drpeyam]

You can always play the video at half speed :)

[@eh9278]

damn, really?

[@michaelchristinarichardson9660]

❤

[@Chsch5]

olaf teaches linear algebra

[@tianhanipah9783]

He looks like Alex Aiono😍😅

[@drpeyam]

Wow what a compliment!

[@Unk0able]

Who encountered the annoying guy of amazon black Friday ads

[@SmileyHuN]

Jordan normal form pls

[@drpeyam]

There’s a video on that already

[@postsldude]

professor, i say it again. You are cute and i cant focus on question due to that 😤😤

[@AbhishekSharma-ir1ym]

Kya paglo ki tarah bk rha hai

[@DancingRain]

RedPenGreenPenBluePen :P

[@LunaPaviseSolcryst]

Pro strats: use cubic formula @.@.

[@shokan7178]

First uwu

[@rahmanabd8287]

Make it simple.soo boring

[@drpeyam]

I have a 2x2 version

[@Titurel]

@@drpeyam don’t listen to him. You’re video are so exciting I eat popcorn when I watch them😊

[@eng_nasurhasan7619]

Amazing