Unitary matrix

A complex matrix is unitary when $U^{†}U=U{U}^{†}=I$. Its columns form an orthonormal basis, and it preserves inner products and norms.

A **unitary matrix** is a complex square matrix \( U \) that satisfies the condition: \[ U^\dagger U = U U^\dagger = I \] where \( U^\dagger \) is the conjugate transpose (also known as the Hermitian transpose) of \( U \), and \( I \) is the identity matrix of the same dimension as \( U \).