Matrix/C/Unitary group/Definition

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

${\displaystyle {}{{\overline {M}}^{\text{tr}}}M=E_{n}\,}$

is called a unitary matrix. The set of all unitary matrices is called the unitary group; it is denoted by

${\displaystyle {}\operatorname {U} _{n}\!={\left\{M\in \operatorname {GL} _{n}\!{\left(\mathbb {C} \right)}\mid {{\overline {M}}^{\text{tr}}}M=E_{n}\right\}}\,.}$