If you have a matrix, and raise it to the power n, what would be the effect on the eigenvalues and the eigenvectors?

Thanks

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- Mar 20th 2010, 06:56 AMllamagoogleEigenvalues and Eigenvectors raised to a power.
If you have a matrix, and raise it to the power n, what would be the effect on the eigenvalues and the eigenvectors?

Thanks - Mar 20th 2010, 10:24 AMtonio
- Mar 20th 2010, 11:22 AMllamagoogle
Thank you,

Where can I find how to prove this? - Mar 20th 2010, 12:55 PMtonio

In your head (honest: the proof is very easy), but I guess books in algebra or linear algebra must deal with this, though I think there's a good chance it'll be an exercise because, as already said, it is very easy. Have you REALLY tried to prove it by yourself already?

Tonio