Unitary Operator

A **unitary operator** is a linear operator ( U ) on a complex vector space that satisfies ( U^\dagger U = UU^\dagger = I ), meaning it preserves inner products. In simpler terms, it preserves the **length** and **angle** between vectors—so it represents a **reversible, norm-preserving transformation**. In quantum mechanics, unitary operators describe the evolution of isolated systems because they conserve probability.