  In this paper, a new kind of resultant, called the determinantal resultant,
is introduced. This operator computes the projection of a determinantal variety
under suitable hypothesis. As a direct generalization of the resultant of a
very ample vector bundle, it corresponds to a necessary and sufficient
condition so that a given morphism between two vector bundles on a projective
variety X has rank lower or equal to a given integer in at least one point.
First some conditions are given for the existence of such a resultant and it is
showed how to compute explicitly its degree. Then a result of A. Lascoux is
used to obtain it as a determinant of a certain complex. Finally some more
detailed results in the particular case where X is a projective space are
exposed.
