Eigenvectors

Definition

An eigenvalue of a matrix $A$ can be obtained by

$$Ae=\lambda e$$

where the $\lambda$ is the corresponding eigenvalue of the eigenvector.

One can interpret eigenvector as decomposing the matrix into independent pieces. See Eigendecomposition.

Definition

A normalized eigenvalue $e_n$ can be obtained by

$$\frac{e_i}{|e_i|}$$