His enthusiasm makes this feel like an exciting adventure.

adorable teacher, effectively learning, Thank you!!

@drpeyam

4 жыл бұрын

You’re welcome! 😄

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

This is a great explanation, thank you!

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 ?

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!!

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

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

You have a strong positive vibe💪

love your enthusiasm about lin algebra

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

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

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

I love this guy's energy

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.

love your attitude!!

Good tutorial on diagonalization. Thank you

my best reagrades and respect from egypt

Thank you. Great video.

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

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

great vid👌

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.

that sign mistake solution was nice.

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.

he is super excited. great video.

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

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

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.

Thank you very much sir

Thank you very much

Amazing

Great Work

Why not factor by grouping at 6:30?

What is the condition for a matrix to be diagonalizable?

@Debg91

5 жыл бұрын

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

5 жыл бұрын

Basically enough eigenvectors :)

@TheMauror22

5 жыл бұрын

Is the diagonal matrix unique for the other matrix?

@war_reimon8343

5 жыл бұрын

Determinant non-zero

How about synthetic division showing only coefficients?

@drpeyam

5 жыл бұрын

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

Thanks for the video

@drpeyam

2 жыл бұрын

Welcome :)

If a matrix is diagonizable then it has eigenvalues?

@drpeyam

5 жыл бұрын

Yeah

you look really happy lol

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

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

@drpeyam

2 жыл бұрын

❤️

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.

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

@drpeyam

5 жыл бұрын

What’s that?

@drpeyam

5 жыл бұрын

Sounds like Fubini, haha

@aryanjain9957

5 жыл бұрын

@@drpeyam Its basically synthetic division

@rodrigogimenez8385

5 жыл бұрын

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

@rodrigogimenez8385

5 жыл бұрын

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

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

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

2 жыл бұрын

Never heard of this other method :)

Why divide by lambda - 1 during long division?

@drpeyam

3 жыл бұрын

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

@Titurel

3 жыл бұрын

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

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

@hellheaven4167

3 ай бұрын

Show the time so we can find the issue

Thank u sir ❤️

Thanks sir

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

5 жыл бұрын

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

@mimithewienerdog6928

5 жыл бұрын

@@drpeyamHaha! Thanks!

god bless you

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

@drpeyam

3 жыл бұрын

Definitely LOL

Is this really so much fun for you my man?

@drpeyam

2 жыл бұрын

Yes it is!

❤

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

10:54

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

2 жыл бұрын

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

@MonkoGames

2 жыл бұрын

@@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.

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

@drpeyam

4 жыл бұрын

You can always play the video at half speed :)

@eh9278

4 жыл бұрын

damn, really?

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

3 жыл бұрын

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

Jordan normal form pls

@drpeyam

5 жыл бұрын

There’s a video on that already

He looks like Alex Aiono😍😅

@drpeyam

3 жыл бұрын

Wow what a compliment!

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

RedPenGreenPenBluePen :P

olaf teaches linear algebra

Pro strats: use cubic formula @.@.

First uwu

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

Who encountered the annoying guy of amazon black Friday ads

Kya paglo ki tarah bk rha hai

Make it simple.soo boring

@drpeyam

3 жыл бұрын

I have a 2x2 version

@Titurel

3 жыл бұрын

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

Amazing

Thank u sir...♥️

@colloupdated

3 жыл бұрын

u are welcomed