  To demonstrate that matrices of seesaw type lead to a hieararchy in the
neutrino masses, i.e. that there is a large gap in the singular spectrum of
these matrices, one generally uses an approximate block-diagonalization
procedure. In this note we show that no approximation is required to prove this
gap property if the Courant-Fisher-Weyl theorem is used instead. This simple
observation might not be original, however it does not seem to show up in the
literature. We also sketch the proof of additional inequalities for the
singular values of matrices of seesaw type.
