The Special Unitary Group#
Theorem: The Special Unitary Group
Let \((V, \langle \cdot, \cdot \rangle)\) be a finite-dimensional complex inner product space.
The set of all unitary transformations \(f: V \to V\) whose determinant is \(+1\) form a subgroup of the unitary group.
Definition: The Special Unitary Group
We call this subgroup the special unitary group.
Notation
We denote the special unitary group on \(V\) by \(\operatorname{SU}(V)\). When \(V\) is the complex vector space \(\mathbb{C}^n\), we also write \(\operatorname{SU}(n, \mathbb{C})\).
Proof
TODO