Range of a linear transformation

$$\text{Range}(L)=\{L(\vec{x})|\vec{x}\in {\mathbb{R}}^n\}$$

• The set of all outputs of the transformation $L$.
• Since $L:{\mathbb{R}}^n\to {\mathbb{R}}^m$ ⇒ $\text{Range}(L)\subseteq {\mathbb{R}}^m$.

Again, translating to matrix-ish notation:

• Range is the same as the column space.