My question is: if $\lambda_1,\lambda_2……,\lambda_s$ are all the eigenvalues of the linear transformation $\mathbb{A}$, whether $\lambda_1^k,\lambda_2^k,……,\lambda_s^k$ are all the eigenvalues of $\mathbb{A^k}$.
We can easily know that the $\lambda_1^k,\lambda_2^k,……,\lambda_s^k$ are indeed the eigenvalues of $\mathbb{A^k}$, and if $s=n$，then they could be all the eigenvalues, but if $s\neq n?$ Whether or not?
I think it's right actually. And any help is appreciated.
