# Definition The special linear group $SL(n, \mathbb{F})$ is a [[subgroup]] of the [[general linear group]] $GL(n, \mathbb{F})$. It is defined to be the set of all matrices with entries from $\mathbb{F}$ that additionally have unit [[determinant]]. The determinant condition makes the elements [[Non-singular Matrix|non-singular]] and one can show that $SL(n, \mathbb{F})$ is a subgroup of $GL(n, \mathbb{F})$. Specifically, it is the [[normal subgroup]] of $GL(n, \mathbb{F})$