So I understand that if an nxn matrix has n distinct eigenvalues that you can diagonalize the matrix into [tex]S\LambdaS^{-1}[/tex]. This is important because then this form has lots of good properties (easy to raise to powers, etc)(adsbygoogle = window.adsbygoogle || []).push({});

So when there are not n distinct eigenvalues, you then solve

[tex](A-\lambda_n)x_n = x_{n-1} [/tex]

Why is this exactly? Also, it is then true that [tex](A-\lambda_n)^2 x= 0 [/tex]. I don't follow why that is either.

I believe all this has to do with the Jordan form. I read this http://en.wikipedia.org/wiki/Jordan_form but I didn't follow some of it. Under the "Example" section, it says "the equation [tex] Av = v[/tex] should be solved". What is that equation for?

I am a EE not a mathematician so please keep your responses at my level! haha. I'm just looking for a "whats the point" kind of explanation.

Thanks!

Dave

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# Generalized Eigenvectors

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