What are eigenvalues and where are they useful in?

Question

goformit100 · Answer

@ParthKohli

turingtest · Answer

They are useful for solving systems of differential equations for one thing

turingtest · Answer

http://tutorial.math.lamar.edu/Classes/LinAlg/EVals_Evects.aspx http://tutorial.math.lamar.edu/Classes/DE/SolutionsToSystems.aspx

anonymous · Answer

Why are they more useful than solving DE normally?

turingtest · Answer

how do you solve systems of DE's without them?

turingtest · Answer

oh you mean with renaming the variables and such...

turingtest · Answer

I hate that way, to much integration

anonymous · Answer

It's just that I've never encountered differential equations with matrices involved

turingtest · Answer

check out this and the next two sections: http://tutorial.math.lamar.edu/Classes/DE/RealEigenvalues.aspx

turingtest · Answer

that covers all three cases

anonymous · Answer

Oh- scratch that, I've just never encountered systems of DE so far. Is their treatment with matrices much the same as systems of linear equations?

anonymous · Answer

By linear, I mean y=mx+c

turingtest · Answer

yes, very similar 
(so long as it is a linear system of DE's of course)
you should really just read the whole link though to elucidate all the subtleties

anonymous · Answer

Alright then, thanks.

turingtest · Answer

welcome