Eigenvalues of a sum of power of a matrix $A$ is defined as a real $n×n$ matrix. $B$ is defined as:
$$B=A+A^2+A^3+A^4+ \dots +A^n$$
What's the relation between eigenvalues of $A$ and eigenvalues of $B$?
Can anyone give me some materials?

HINT
If $A$ is diagonalizable, say $A = VDV^{-1}$ then
$$
B = \sum_{k=1}^n \left(VDV^{-1}\right)^k
  = \sum_{k=1}^n VD^kV^{-1}
  = V \left(\sum_{k=1}^n D^k \right)V^{-1}
$$
and $D$ is a diagonal matrix. Can you take it from here?
