---
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 \(T|_{U} \in \mathcal{L}(U)\)
