Cayley-Hamilton Theorem [Control Bootcamp]

Here we describe the Cayley-Hamilton Theorem, which states that every square matrix satisfies its own characteristic equation. This is very useful to prove results related to controllability and observability.
These lectures follow Chapter 8 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com...
Chapters available at: databookuw.com/...
Book Website: databookuw.com
Brunton Website: eigensteve.com
This video was produced at the University of Washington

[@oshomasamson1906]

"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

[@giorgospanagiotidis3134]

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..

[@spoopedoop3142]

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.

[@NoobSaibot123]

😆

[@badnoodlez]

@@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.

[@dacianbonta2840]

more than one way to shuck an oyster

[@kpadjisamuel2968]

😂😂

[@robbiewilliamson9783]

Your enthusiasm is contagious. Great video :)

[@Eigensteve]

Glad you liked it!

[@ulisespachecosanchez5058]

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.

[@suryagurajapu8474]

How can they write in reverse

[@hierismail]

He mentioned in a different video that he is lefthanded. My guess? He writes just normaly and then mirrors the video.

[@helpmireach66subwith0video9]

Because this video is flipped(edited)

[@helpmireach66subwith0video9]

​@@hierismaillol this video is flipped

[@gahozomuhamedi7287]

Sagt feyjyu maniaba so, it is so interesting to hear from you thanks sedurufu karanga monira you deserve 5 star

[@rijugoswami600]

It is true for every square matrix

[@sanjanavijayshankar5508]

Favorite theorem ever!

[@Eigensteve]

One of my favorites too... so powerful

[@generalginger7804]

Nerd

[@bharathiarumugam263]

Every square matrix satifies it's own characteristic equation

[@gargantua1]

Hi! Could you explain what was the square matrix that Cayley Hamilton does not work on?

[@charlesbrowne9590]

Emre Yılmaz The C-H theorem is valid for all square matrices, no exceptions. The lecturer was confused by someone who erroneously thought otherwise.

[@KrzysiekWawrytko]

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.).

[@abeershawk5986]

Thank you a thousand times!!!

[@Eigensteve]

You are very welcome!

[@RugnirSvenstarr]

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

[@KrzysiekWawrytko]

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.

[@bau6398]

How did you write that....

[@VidimusWolf]

Hi! Thank you very much for the lesson, I love your passion and it really makes everything more easily understandable!

[@ritobanghosh7453]

Agree, I understood it clearly.

[@MATHSMANHARSAN]

Superb sir.kzbin.info/www/bejne/fZK8lYKsfdStkJo This is also the best way to proof

[@Eigensteve]

You are welcome!

[@fathimathusafa1975]

Thank you a thousand times.... 😍😍

[@tobyouyang3463]

This is honest to goodness art!

[@raincloud763]

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.

[@shridharambady2069]

Is there an error at 3:56? Shouldn't there be a negative term?

[@3rddegreeyt144]

(-1)^n cuz in matrix 3x3 the polynomial come with -x³ and in polynomial of 2x2 matrix +x² you get it

[@siddhartha5186]

are u writing in reverse

[@playerunknownbattlegraound]

How is this possible guy's... That's amazing👍 How wrote you.... 🤪🤪🤯

[@saunakroychowdhury5990]

how do they use such board? If anyone can explain

[@helpmireach66subwith0video9]

Its just class but flipped the video after shot

[@dhamodharreddyguthikonda2260]

Why you written alpha1(t) up to so on in e power at

[@jiayiliu9128]

great video! thanks you

[@Eigensteve]

Glad you liked it!

[@abdulfatahmohamoud1146]

Remarkble video .

[@Listen_bros]

You saying ... is cool 😁

[@MATHSMANHARSAN]

Nice

[@Eigensteve]

Thanks

[@MATHSMANHARSAN]

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?

[@cankandamar]

Somebody explain how he writes that way

[@anda9169]

The video is inverted

[@allandogreat]

Thanks....

[@bharathiarumugam263]

Hey man!!! How cool you are !!!😍 & Handsome too❤love the way you are 😌

[@madhurwagh5418]

How the hell ya'll write backwards!!?

[@PaulWintz]

They're writing forwards. The video is mirrored.

[@v.a2282]

How is he writing backwards?! Am i tripping? It's 2am

[@md-mahfuzur-rahman]

❤❤❤

[@fynn4310]

Falschgeld

[@fiesescheiwen134]

tru

[@MTNtf2]

helal lan sana

[@MATHSMANHARSAN]

Superb

[@fiesescheiwen134]

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?!?!

[@electro.engineering]

Ja, es gilt für alle nxn Matrizen, deren Einträge aus einem kommutativen Ring (Z, R, C, etc...) kommen.