  In his celebrated paper "Generic projections", John Mather has shown that
almost all linear projections from a submanifold of a vector space into a
subspace are transverse with respect to a given modular submanifold. In this
paper, an improvement of Mather's result is stated. Namely, we show that almost
all linear perturbations of a smooth mapping from a submanifold of
$\mathbb{R}^m$ into $\mathbb{R}^\ell$ yield a transverse mapping with respect
to a given modular submanifold. Moreover, applications of this result are
given.
