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I understand one of the motivations for eigenvalues/vectors is when you need

to compute A^k * x. So we like to write,

A = C*D*C^-1 and then A^k = C * D^k * C^-1, and D^k is trivial to compute.

My professor said C^-1 and C can be though of as change of coordinate

matrices. But from which basis? For example, C^-1 would take me from

*some* basis to the basis of eigenvectors. But what is this *some* basis?

Is it assumed that everything is coordinitized relative to some basis B in

R^n. And then I want to change to the basis of eigenvectors B'?

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# Motivations for eigenvalues/vectors

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