Eigenvector

linear-algebra

Definition

Eigenvector

An eigenvector is a vectors that has an eigenvalue.

Example

Matrix Example

To find the eigenvectors of an eigenvalue ${\lambda }_1=4$ for a square matrix $A\in F^{n\times n}$, the homogeneous linear system of equation must be solved:

$$(4\cdot I_2-A)\cdot \mathbf{x}=\left[\begin{array}{cc}3& -2\\ -3& 2\end{array}\right]\cdot \mathbf{x}=0$$