> [!NOTE] Definition (Image & Kernel) > Let $\varphi:V \to W$ be a [[Linear maps|linear map]]. The [[Image of a set under a function|image]] of $\varphi$, denoted $\text{Im}(\varphi)$, is the subset of $W$ $\text{Im}(\varphi) = \{ \varphi(v) \mid v \in V \}$ > # Properties By [[Image of Linear Map is Subspace of Codomain]], ...