# Definition(s) > [!NOTE] Definition 1 (Affine map from $\mathbb{R}^n$ to $\mathbb{R}^k$ ) > A map $T:\mathbb{R}^{n}\to \mathbb{R}^{k}$ is affine if it has the form $T(\underline{x})=L(\underline{x})+\underline{b}$for all $\underline{x}\in \mathbb{R}^{n}$ for some [[Linear maps|linear map]] $L:\mathbb{R}^{n}\to \mathbb{R}^{k}$ and $\underline{b}\in \mathbb{R}^k$ > [!Example] Example > Contents # Properties(s) By [[Set of Invertible Affine Transformations on Real n-Space Form A Group wrt Semi Direct Product Law]]. # Application(s) **More examples**: # Bibliography