Matrix/C/Special unitary group/Definition

A unitary ${\displaystyle {}n\times n}$-matrix ${\displaystyle {}M\in \operatorname {GL} _{n}\!{\left(\mathbb {C} \right)}}$ fulfilling

${\displaystyle {}\det M=1\,}$

is called a special unitary matrix. The set of all special unitary matrices is called the special unitary group; it is denoted by ${\displaystyle {}\operatorname {SU} _{n}}$.