Matrix/C/Unitary group/Definition

Unitary group

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

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

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

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