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 $\phi$ is defined as:


 * $\ker\left({\phi}\right) := \phi^{-1} \left({\left\{{e_H}\right\}}\right)$.

where $\phi^{-1}\left({S}\right)$ denotes the preimage of $S$ under $\phi$.

Also see

 * Definition:Null Space


 * Kernel of Linear Transformation contains Zero Vector
 * Kernel of Linear Transformation is Null Space of Matrix Representation