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:


 * $\map \ker \phi := \phi^{-1} \sqbrk {\set {e_H} }$.

where $\phi^{-1} \sqbrk S$ 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