> [!NOTE] Definiton > Let $A$ be a [[Real Square Matrices|real square matrix]] of order $n.$ Let $\lambda$ be an [[Eigenpair of Real Square Matrix|eigenvalue]] of $A.$ The subspace $E_{\lambda}=\{ v\in \mathbb{R}^{n} \mid A\underline{v} = \lambda \underline{v} \}$is called the **eigenspace** of $A$ corresponding to $\lambda.$