  We study the essentially isolated determinantal singularities (EIDS), defined
by W. Ebeling and S. Gusein-Zade, as a generalization of isolated singularity.
We prove in dimension $3$ a minimality theorem for the Milnor number of a
generic hyperplane section of an EIDS, generalizing previous results by J.
Snoussi in dimension $2$. We define strongly generic hyperplane sections of an
EIDS and show that they are still EIDS.
  Using strongly general hyperplanes, we extend a result of L\^e D. T.
concerning constancy of the Milnor number.
