Solution
= Solution
The first block is the <companion matrix> of $t-3$. The last block is the <companion matrix> of $f(t)=t^3-3t^2+9t-27=(t-3)(t^2+9)$. Since $t-3$ divides $f$, these are the ordered <invariant factors of a linear operator>. Thus
$$
\boxed{m_\alpha(t)=(t-3)(t^2+9),\qquad\chi_\alpha(t)=(t-3)^2(t^2+9).}
$$
The <minimal polynomial> is the largest invariant factor, and the <characteristic polynomial> is their product.