Since the determinant of a unitary matrix is a complex number with norm 1, the determinant gives a group homomorphism See more

2-out-of-3 property
The unitary group is the 3-fold intersection of the orthogonal, complex, and symplectic groups:
Thus a unitary … See more

From the point of view of Lie theory, the classical unitary group is a real form of the Steinberg group $${\displaystyle {}^{2}\!A_{n}}$$, which is an algebraic group that arises from the combination of the diagram automorphism of the general linear group … See more

The classifying space for U(n) is described in the article Classifying space for U(n). See more

The unitary group U(n) is endowed with the relative topology as a subset of M(n, C), the set of all n × n complex matrices, which is itself … See more

In the language of G-structures, a manifold with a U(n)-structure is an almost Hermitian manifold. See more

The unitary groups are the automorphisms of two polynomials in real non-commutative variables:
These are easily … See more