The Cayley-Hamilton Theorem is Easy with F[x]-Modules

Invariant factors proof: • Proof: Structure Theor...
Characteristic polynomial explanation: • How the Matrix Charact...
Intro to F[x]-modules: • Introduction and Deriv...
The Cayley-Hamilton theorem says that every matrix is a root of its own characteristic polynomial, det(xI-A). With all of our knowledge of F[x]-modules, the proof is simple! This video is an explanation of how we reach this important result in linear algebra.
Ring & Module Theory playlist: • Ring & Module Theory
0:00 Proof
6:32 Example
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez

[@robertflynn6686]

Good job on that.🥸 This note self annhilates

[@sanelprtenjaca9776]

Which book did you use for the Group theory?

[@MuPrimeMath]

Dummit and Foote, but I mostly learned from course lectures

[@tomkerruish2982]

Are you doing a SURF?

[@mohammedmadani7277]

What is the inverse function of x/lnx with proof

[@Stormneo]

Posted 2 mins ago. 1 like. 0 views. Good job youtube

[@crackindenpockets6211]

i dont get why f1*...*fm equals the characteristic polynomial

[@MuPrimeMath]

See kzbin.info/www/bejne/oHTXZ6CIaLanhs0

[@tomkerruish2982]

I sure hope you're taking Ma 5 (if not Ma 120), or you're going to be soooo bored next year.

[@MuPrimeMath]

I'm learning this stuff in Math 5 right now!

[@tomkerruish2982]

@@MuPrimeMath You're doing a bang-up job of relating it! (You cool cats still say "bang-up job", right? Ooh, I think I can feel my kids instinctively cringe from miles away.)

[@Tomaplen]

RIP channel?