Definition:Special Unitary Group

Definition

Let $n$ be a positive integer.

The special unitary group $\operatorname {SU}_n$ is the group of all $n \times n$ unitary matrices with determinant $1$:

$\operatorname {SU}_n = \operatorname U_n \cap \map {\operatorname {SL}_n} \C$

where:

$\operatorname U_n$ is the unitary group

$\map {\operatorname {SL}_n} \C$ is the special linear group over the complex numbers.

Also see

• Definition:Unitary Group
• Definition:Special Orthogonal Group

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