Solution
= Solution
The <characteristic polynomial> of $A$ is
$$
\chi_A(t)=\det(tI-A).
$$
A <scalar> $\lambda\in\mathbb C$ is an <eigenvalue> when there is a nonzero <vector> $v$ such that
$$
Av=\lambda v.
$$
Such a $v$ is an <eigenvector> belonging to $\lambda$. Equivalently, $\lambda$ is a root of $\chi_A$ and the corresponding <eigenvectors> are the nonzero elements of $\ker(A-\lambda I)$.