Matrix/K/Special linear group/Definition

Special linear group

For a field ${}K$, and ${}n\in \mathbb {N} _{+}$, the set of all invertible ${}n\times n$-matrices over ${}K$ with

${}\det M=1\,$

is called the special linear group over ${}K$. It is denoted by ${}\operatorname {SL} _{n}\!{\left(K\right)}$.