# Math Help - Eigenvalues and Eigenvectors raised to a power.

1. ## Eigenvalues 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

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

Thanks

$Av=\lambda v\Longrightarrow A^nv=\lambda^nv\,,\,\,\forall\,n\in\mathbb{N}$ . You can easily prove this by induction.

If the matrix is invertible the above is extendable to negative powers, too.

Tonio

3. Thank you,
Where can I find how to prove this?