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