  In this paper we show that determinantal ideals of generic matrices are
Knutson ideals. This fact leads to a useful result about Gr\"obner bases of
certain sums of determinantal ideals. More specifically, given
$I=I_1+\ldots+I_k$ a sum of ideals of minors on adjacent columns or rows, we
prove that the union of the Gr\"obner bases of the $I_j$'s is a Gr\"obner basis
of $I$.
