  We study the topological triviality and the Whitney equisingularity of a
family of isolated determinantal singularities. On one hand, we give a
L\^e-Ramanujam type theorem for this kind of singularities by using the
vanishing Euler characteristic. On the other hand, we extend the results of
Teissier and Gaffney about the Whitney equisingularity of hypersurfaces and
complete intersections, respectively, in terms of the constancy of the polar
multiplicities.
