Unitary Operator

linear-algebra

Definition

Unitary Operator

Let be a linear operator on a complex inner product space . The operator is unitary if its adjoint is also its inverse, that is,

where is the identity operator. Equivalently, preserves inner products:

Unitary operators are reversible and norm-preserving.

Properties

Isometric

Unitary operators are isometric, i.e.:

Eigenvalues

Eigenvalues of a unitary operator are unimodular, i.e. it holds that: