# Definition The *kernel* of a [[map]] $f:X \rightarrow Y$ is the set $\{x \in X | f(x) = 0\}$, i.e., it is the set of elements which are mapped to zero. It is denoted $\text{ker}(f)$. If $V$ and $W$ are [[vector space|vector spaces]], then $\text{ker}(f)$ is a [[vector subspace]] of $V$. It is also known as the *null space* of $f$, and $\dim(\text{ker}(f))$ is known as the *nullity* of $f$.