Unitary operators

Unitary operators are fundamental objects in the field of quantum mechanics and linear algebra. They are linear operators that preserve the inner product in a complex vector space. Here’s a more detailed explanation: ### Definition: A linear operator \( U \) is called unitary if it satisfies the following conditions: 1. **Preservation of Norms**: For any vector \( \psi \) in the space, \( \| U\psi \| = \|\psi\| \).