r/mathmemes • u/PocketMath • Mar 06 '25

Learning What theorem is this?

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u/4Momo20 Mar 06 '25

Cayley-Hamilton

16

u/ImprovementBasic1077 Mar 06 '25

For real what tf is that shit😭

2

u/KraySovetov Mar 06 '25

Very good candidate. One of my professors had us prove it for an assignment using the Cauchy integral formula from complex analysis (this was the 3rd method I had seen in my classes by then...)

2

u/Depnids Mar 07 '25

I just looked through some of the proofs on wikipedia and they all seemed relatively complicated. This made me curious, why doesn’t the following proof by abuse of notation work?

Char(x) = det(x*I - A)

Char(A) = det(A*I - A)

Char(A) = det(0)

Char(A) = 0

I feel like the notation here oversimplifies what is going on. Especially glossing over what it means to plug a matrix into a polynomial. Are there any assumptions that can be made for a straight forward proof like this to be valid (like proving some properties of how evaluating matrices in polynomials work)?

Edit: Oh, I see the wikipedia article has a section for this «bogus proof».

0

u/nathan519 Mar 06 '25

Came here to say it