Unitary matrices

A unitary matrix is a complex matrix $U$ satisfying the condition

$U^{\dagger }U=UU^{\dagger }=I_{n}\,$

where $I$ is the identity matrix and $U^{\dagger }$ is the conjugate transpose (also called the Hermitian adjoint) of $U$. Note this condition says that a matrix $U$ is unitary if and only if it has an inverse which is equal to its conjugate transpose $U^{\dagger }\,$

$U^{-1}=U^{\dagger }.$

A unitary matrix in which all entries are real is called an orthogonal matrix.

References

• Unitary matrix entry in Wikipedia