Definition:Kernel of Linear Transformation

Definition
Let $\phi: G \to H$ be a linear transformation where $G$ and $H$ are $R$-modules.

Let $e_H$ be the identity of $H$.

The kernel of $\phi$, denoted $\ker \left({\phi}\right)$, is the subset $\phi^{-1} \left({\left\{{e_H}\right\}}\right)$ of $G$.

Also see

 * Null Space