  The (homogeneous) Essentially Isolated Determinantal Variety is the natural
generalization of generic determinantal variety, and is fundamental example to
study non-isolated singularities. In this paper we study the characteristic
classes on these varieties. We give explicit formulas of their
Chern-Schwartz-MacPherson classes and Chern-Mather classes via standard
Schubert calculus. As corollaries we obtain formulas for their (generic)
sectional Euler characteristics, characteristic cycles and polar classes.
