Justify that for all integer $k \geqslant 1$, $A^k$ is similar in $\mathcal{M}_n(\mathbb{C})$ to a triangular matrix, whose diagonal coefficients we will specify.
Justify that for all integer $k \geqslant 1$, $A^k$ is similar in $\mathcal{M}_n(\mathbb{C})$ to a triangular matrix, whose diagonal coefficients we will specify.