Restriction Operator

Defining a linear map for a smaller domain.

Notation

• $f|S:S\to \mathbb{R}$

Definition

• With $T\in \mathcal{L}(V)$
• With Subspace $W\subset V$
• With $W$ Invariant under $T$
• The restriction operator $T_W:W\to W$ is defined as $T_W(x)=Tx,\forall x\in W$ Note that $T_W\ne T$, as $domain(T_W)=W,domain(T)=V$