Linear transformations and eigenvalues Let $T: \mathbb C^n \rightarrow \mathbb C^n$ be linear. Let $\beta$ and $\gamma$ be any two ordered bases. Prove that the eigenvalues of $[T]_\beta$ and $[T]_\gamma$ are the same. 
Can anyone provide tips/hints in the right direction? I'm struggling as I try to understand this intuitively....thank you

HINT $$det(B - \lambda I_n) = det(A - \lambda I_n)$$ for two similar matrices $A$ and $B$. (Why?)
