Identity Operator

linear-algebra

Definition

Identity Operator

Let $V$ be a vector space. The identity operator, which is linear, is defined by:

$$I(x)=x\forall x\in V$$

Equivalently:

$$⟨Ix,y⟩=⟨x,Iy⟩=⟨Ix,I,y⟩=⟨x,y⟩x,y\in \mathcal{H}$$