The kernel of a [[Homomorphism]] $f: (X, \circ)\to (Y, *)$ is the [[Subset|subset]] $\ker(f) \subseteq X$ that $f$ [[Function|maps]] to $e_Y$ ([[Identity Function|identity]] of $Y$). $\huge \begin{align} f: X \to Y \\ \ker(f) &= \setbuild{x \in X}{f(x) = e_{Y}} \end{align}$ ### Examples - [[Linear Algebra]] / [[Linear Transformation|Linear Maps]] - [[Kernel (Vector Space)]] - [[Group Homomorphism]] - [[Kernel (Groups)]]