Eigenvector

When a vector doesn’t change its direction after multiplying with a matrix, then it’s an eigenvector.

Formally, a vector $v$ is an eigenvector of the matrix $M$ if $M\cdot v=\lambda v$where $\lambda$ is the corresponding eigenvalue.

For example, $\left(\begin{array}{c}1\\ 0\end{array}\right)$ does not change when shear mapping.