Definition:Eigenspace
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Definition
Let $K$ be a field.
Let $V$ be a vector space over $K$.
Let $A : V \to V$ be a linear operator.
Let $I : V \to V$ be the identity mapping on $V$.
Let $\lambda \in K$ be an eigenvalue of $A$.
Let $\map \ker {A - \lambda I}$ be the kernel of $A - \lambda I$.
We say that $\map \ker {A - \lambda I}$ is the eigenspace corresponding to the eigenvalue $\lambda$.
Also see
- Kernel of Linear Transformation is Closed Linear Subspace shows that the eigenspace $\map \ker {A - \lambda I}$ is a closed linear subspace of $V$.
Sources
- 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $14.1$: The Resolvent and Spectrum