Editing Unitary group (section)

=== Special unitary and projective unitary groups ===
[[File:PSU-PU.svg|right]]
{{see also|Special unitary group|Projective unitary group}}

Just as the orthogonal group O(''n'') has the [[special orthogonal group]] SO(''n'') as subgroup and the [[projective orthogonal group]] PO(''n'') as quotient, and the [[projective special orthogonal group]] PSO(''n'') as [[subquotient]], the unitary group U(''n'') has associated to it the [[special unitary group]] SU(''n''), the [[projective unitary group]] PU(''n''), and the [[projective special unitary group]] PSU(''n''). These are related as by the [[commutative diagram]] at right; notably, both projective groups are equal: {{nowrap|1=PSU(''n'') = PU(''n'')}}.

The above is for the classical unitary group (over the complex numbers) – for [[#Finite_fields|unitary groups over finite fields]], one similarly obtains special unitary and projective unitary groups, but in general {{nowrap|PSU(''n'', ''q''<sup>2</sup>) ≠ PU(''n'', ''q''<sup>2</sup>)}}.