Image

$\text{im}(T)=\{T(\vec{x}):\vec{x}\in {\mathbb{R}}^m\}=\text{span}({\vec{v}}_1,\dots ,{\vec{v}}_m)$

• $T:{\mathbb{R}}^m\to {\mathbb{R}}^n$
• Same as the range of a function
• $\text{im}(T)\subseteq {\mathbb{R}}^n$ and $\text{im(T)}$ is a subspace of ${\mathbb{R}}^n$
• Also known as the column space of $A$, where $A$ is a matrix of column vectors representing $T$