  In a multi-level energy system with energy transitions, dark states are
eigenstates of a Hamiltonian that consist entirely of ground states, with zero
amplitude in the excited states. We present several criteria which allows one
to deduce the presence of dark states in a general multi-level system based on
the submatrices of the Hamiltonian. The dark states can be shown to be the
right-singular vectors of the submatrix that connect the ground states to the
excited states. Furthermore, we show a simple way of finding the dark state
involving the determinant of a matrix constructed from the same submatrix.
