Algorithm: determine eigenvectors

Problem

Suppose a matrix

\begin{align*} A \in K^{n \times n} \end{align*}

is given and you have to determine the eigenvectors

for each eigenvalue \(\lambda\) consider the matrix

\begin{align*} \lambda E_n - A \end{align*}

Then a vector is an eigenvector if and only if it lies in the kernel.
Hence determine the kernel.

The kernel is also by Definition the Eigenspace