# Unitary matrices

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