The Kernel of a [[Linear Transformation]] $T$ is the [[Subset]] of the [[Domain]] of $T$ whose [[Image]] is the [[Zero Vector]]. $\huge \op{ker}(T) = \left\{\vec x \in \R^m \left\vert\, T(\vec x) =\vec 0\right.\right\} $ The Kernel of a [[Linear Transformation]] has a minimum [[Cardinality]] of $1$, as $\vec 0 \mapsto \vec 0$ for any [[Linear Transformation]]. The [[Kernel]] is equal to the [[Set]] containing only the [[Zero Vector]] [[Biconditional|If and only If]] the [[Function|Transformation]] is [[Injective|One-to-One]].