Group representation

Unitary representation

A unitary representation of is a group homomorphism into the unitary group #m/def/rep2 where is a complex inner product space. Thus is a group representation carried by such that

for all and where is the inner product.

Properties

• Every finite complex representation of a compact group is equivalent to a unitary representation.
• The orthogonal complement of an invariant subspace under a unitary operator is invariant

#state/tidy | #lang/en | #SemBr