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