Eigenvector & Eigenvalue

An Eigenvector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear transformation.

An eigenvector $\mathbf{v}$ of a linear transformation $T$ is scaled by a constant factor $\lambda$ when the linear transformation is applied to it: $T\mathbf{v}=\lambda \mathbf{v}$. Where $\lambda$ is the eigenvalue.

$Av=\lambda v$

• $A$: A square matrix representing the linear transformation.
• $v$: The non-zero eigenvector.
• $\lambda$: The corresponding eigenvalue.