> [!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 $A.$ Let $E_{\lambda}$ denote the **[[Eigenspace of Real Square Matrix Corresponding to Eigenvalue|eigenspace]]** of $A$ corresponding to $\lambda.$ The geometric multiplicity of $\lambda$ is given by the [[Dimension of Finite Dimensional Real Vector Space|dimension]] of $E_{\lambda}.$