Range

definitionabstract-algebra

Definition

For $T\in \mathcal{L}(V,W)$, the range of $T$ is given by,

$$\mathrm{range}T=\left\{Tv\mid v\in V\right\}.$$

Properties

• For a map $T:V\to W$, $\mathrm{range}T$ is a subspace of $W$.

Examples