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@jemoka / Jemoka Knowledge Base / wiki/concepts/map_restriction_operator.md
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--- title: "map restriction operator" type: concept related: [Invariant Subspace] source: https://www.jemoka.com/posts/kbhmap_restriction_operator/ confidence: high status: active --- Suppose \(T \in \mathcal{L}(V)\), and \(U \subset V\), an invariant subspace under \(T\). Then: \begin{equation} T|_{U}(u) = Tu,\ \forall u \in U \end{equation} where \(T|_{U} \in \mathcal{L}(U)\)