I 've watched about 5 videos of C-H theorem and each of you is explaining it differently.. I think you should all gather together and talk this through..
C-H is a big theorem that has found it's way into many different applications. Each of these will have a different interpretation based on what it is used for in their field, and the "best interpretation" is usually dependent on context or is whichever melds with your psychology.
@@spoopedoop3142 The only real interpretation is that you can use the eigenvalues of a matrix to form an interpolation problem. E.g matching on eigenvalues. Find the inverse or any power in terms of the characteristic equation is just a special case of mapping onto analytic functions.
This is one of the most important lessons that we need to know and understand details and where they are doing intepretation of differentes points for to get the solution in this particular form..thank you..very interesting....thank´s.
Of course, the guy is wrong. Someone told him that there are some square matrices that do not satisfy their own characteristic polynomial and he has repeated this false claim. The C-H is a perfect theorem and holds for every matrix (as long as it is a matrix with coefficients in a commutative ring, such as Z, R, C etc.).
n here is still the dimentions of the state right? I got pretty confused trying to follow this one, the others have been fantastic so far though. Edit: and alpha is the coefficient of that bit of the characteristic polynomial I think? is there a fancy way to get that without going the long way around and multiplying out A
The guy is obviously wrong when claiming that Caley-Hamilton theorem is not true for some matrices (of course he did not present any such counterexample). Every matrix satisfies its characteristic equations provided that its entries are in commutative ring. But this is the case of reals, complex or integer numbers. I do not thing that he may have thought of the matrices with, let’s say, quaternions elements. This is quite a different story - there are even problems with defining a determinant for such non-commutative fields.
I understand that matrix A's order can by lowered Cayley-Hamilton theorem, but what about the alpha term that is multiplied to A. Can the order of t in the alpha term also be reduced by some fascinating theory? Anyway thank you for the lecture sir.
![Reachability and Controllability with Cayley-Hamilton [Control Bootcamp]](http://i.ytimg.com/vi/gpIhGAUoeNY/mqdefault.jpg)
![Reachability and Controllability with Cayley-Hamilton [Control Bootcamp]](/img/tr.png)
I 've watched about 5 videos of C-H theorem and each of you is explaining it differently.. I think you should all gather together and talk this through..
C-H is a big theorem that has found it's way into many different applications. Each of these will have a different interpretation based on what it is used for in their field, and the "best interpretation" is usually dependent on context or is whichever melds with your psychology.
😆
@@spoopedoop3142 The only real interpretation is that you can use the eigenvalues of a matrix to form an interpolation problem.
E.g matching on eigenvalues. Find the inverse or any power in terms of the characteristic equation is just a special case of mapping onto analytic functions.
more than one way to shuck an oyster
😂😂
"If you see Hamilton's name, you know it's gonna be a big deal"
As an F1 fan, i can confirm he's correct
Your enthusiasm is contagious. Great video :)
Glad you liked it!
How can they write in reverse
He mentioned in a different video that he is lefthanded.
My guess? He writes just normaly and then mirrors the video.
Because this video is flipped(edited)
@@hierismaillol this video is flipped
This is one of the most important lessons that we need to know and understand details and where they are doing intepretation of differentes points for to get the solution in this particular form..thank you..very interesting....thank´s.
Hi! Could you explain what was the square matrix that Cayley Hamilton does not work on?
Emre Yılmaz The C-H theorem is valid for all square matrices, no exceptions. The lecturer was confused by someone who erroneously thought otherwise.
Of course, the guy is wrong. Someone told him that there are some square matrices that do not satisfy their own characteristic polynomial and he has repeated this false claim. The C-H is a perfect theorem and holds for every matrix (as long as it is a matrix with coefficients in a commutative ring, such as Z, R, C etc.).
n here is still the dimentions of the state right? I got pretty confused trying to follow this one, the others have been fantastic so far though.
Edit: and alpha is the coefficient of that bit of the characteristic polynomial I think? is there a fancy way to get that without going the long way around and multiplying out A
Is there an error at 3:56? Shouldn't there be a negative term?
(-1)^n cuz in matrix 3x3 the polynomial come with -x³ and in polynomial of 2x2 matrix +x² you get it
How did you write that....
Sagt feyjyu maniaba so, it is so interesting to hear from you thanks sedurufu karanga monira you deserve 5 star
It is true for every square matrix
how do they use such board? If anyone can explain
Its just class but flipped the video after shot
Favorite theorem ever!
One of my favorites too... so powerful
Nerd
The guy is obviously wrong when claiming that Caley-Hamilton theorem is not true for some matrices (of course he did not present any such counterexample). Every matrix satisfies its characteristic equations provided that its entries are in commutative ring. But this is the case of reals, complex or integer numbers. I do not thing that he may have thought of the matrices with, let’s say, quaternions elements. This is quite a different story - there are even problems with defining a determinant for such non-commutative fields.
Why you written alpha1(t) up to so on in e power at
Every square matrix satifies it's own characteristic equation
Hi! Thank you very much for the lesson, I love your passion and it really makes everything more easily understandable!
Agree, I understood it clearly.
Superb sir.th-cam.com/video/GaYdOvHozZ8/w-d-xo.html
This is also the best way to proof
You are welcome!
I understand that matrix A's order can by lowered Cayley-Hamilton theorem, but what about the alpha term that is multiplied to A. Can the order of t in the alpha term also be reduced by some fascinating theory? Anyway thank you for the lecture sir.
are u writing in reverse
Thank you a thousand times!!!
You are very welcome!
This is honest to goodness art!
Thank you a thousand times.... 😍😍
How is this possible guy's...
That's amazing👍
How wrote you....
🤪🤪🤯
Nice
Thanks
Sir.i am also have a channel in name of ADVANCED MATHEMATICS. I need to know that app you have used in editing this video.may i know the name please?
How the hell ya'll write backwards!!?
They're writing forwards. The video is mirrored.
Somebody explain how he writes that way
The video is inverted
great video! thanks you
Glad you liked it!
Remarkble video .
How is he writing backwards?! Am i tripping? It's 2am
Thanks....
Hey man!!! How cool you are !!!😍
& Handsome too❤love the way you are 😌
You saying ... is cool 😁
❤❤❤
Falschgeld
tru
helal lan sana
Superb
Imagine man schaut Formel 1 und denkt sich ich mach zu dem Hamilton ein Video! Gilt das jetzt für alle Matrizen oder nicht du kek?!?!
Ja, es gilt für alle nxn Matrizen, deren Einträge aus einem kommutativen Ring (Z, R, C, etc...) kommen.