Definition:Eigenvector/Real Square Matrix

Definition
Let $\mathbf A$ be a square matrix of order $n$ over $\R$.

Let $\lambda \in \R$ be an eigenvalue of $\mathbf A$.

We say that a non-zero vector $\mathbf v \in \R^n$ is an eigenvector corresponding to $\lambda$ if:


 * $\mathbf A \mathbf v = \lambda \mathbf v$

Also see

 * Definition:Eigenvalue of Real Square Matrix