image

$\operatorname{im}(T)$ — every output a linear transformation can produce.

For $T:V\to W$ , the image (or range), written $\operatorname{im}(T)$ , is $\{T(\mathbf v):\mathbf v\in V\}\subseteq W$ — a subspace of $W$ . When $A$ is $T$ 's standard matrix, $\operatorname{im}(T)=\operatorname{Col}(A)$ : the image of a linear transformation and the column space of its standard matrix are the same subspace.