Kernel

Definition: Kernel

Let $(V,F,+,\cdot )$ and $(W,F,+,\cdot )$ be vector spaces.

The kernel of a Linear Transformation $T:V\to W$ is the set of all vectors $\mathbf{v}\in V$ which the transformation sends to the zero vector in $W$:

$$\ker (L)\stackrel{\text{def}}{=}\{\mathbf{v}\in V\mid T(\mathbf{v})=0_W\}$$