  In 1990, Romero presented a beautiful formula for the projection onto the set
of rectangular matrices with prescribed row and column sums. Variants of
Romero's formula have been rediscovered by Khoury and by Glunt, Hayden, and
Reams, for bistochastic (square) matrices in 1998.
  These results have found various generalizations and applications. In this
paper, we provide a formula for the more general problem of finding the
projection onto the set of rectangular matrices with prescribed scaled row and
column sums. Our approach is based on computing the Moore-Penrose inverse of a
certain linear operator associated with the problem. In fact, our analysis
holds even for Hilbert-Schmidt operators and we do not have to assume
consistency. We also perform numerical experiments featuring the new projection
operator.
