I have found these two apparently contradicting remarks about projection matrices:
1) A matrix $P$ is idempotent if $PP = P$. An idempotent matrix that is also Hermitian is called a projection matrix.
2) $P$ is a projector if $PP = P$. Projectors are always positive which implies that they are always Hermitian.
Which of both is correct? Is a matrix $P$ that verifies $PP=P$ always Hermitian?