Unitary operator

Summary

A unitary operator is a bounded linear operator $U$ on a Hilbert space with $U^*U = UU^* = I$. Equivalently, it is a surjective linear map that preserves the inner product. Unitary operators are the isomorphisms of Hilbert spaces, so two operators that differ by conjugation with a unitary operator have the same properties. They extend unitary matrices to infinite dimensions and describe the time evolution in quantum mechanics.