unitary matrix

\(U^\dagger U = I\)

• This is the complex analogue of a orthogonal matrix, which corresponds with rotations and reflections (see wikipedia, see also SO(3), which is just rotations)

• A unitary product preserves the inner product. So if \(X\) and \(Y\) are inner product spaces, then

\(\braket{x\mid y}_X = \braket{Ux \mid Uy}\)