  We show that the Bethe vectors are non-zero vectors in the sl_{r+1} Gaudin
model. Moreover, we show that the norm of a Bethe vector is equal to the
Hessian of the corresponding master function at the corresponding
non-degenerate critical point. This result is a byproduct of functorial
properties of Bethe vectors studied in this paper.
  As other byproducts of functoriality we show that the Bethe vectors form a
basis in the tensor product of several copies of first and last fundamental
sl_{r+1} modules and we show transversality of some Schubert cycles in the
Grassmannian of r+1-dimensional planes in the space of polynomials of one
variable of degree not greater than d.
