Houjun Liu

map restriction operator

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