Euler obstruction of essentially isolated determinantal singularities

We study the Euler obstruction of essentially isolated determinantal singularities (EIDS). The EIDS were defined by W. Ebeling and S.M. GuseÄ­n-Zade [15], as a generalization of isolated singularity. We obtain some formulas to calculate the Euler obstruction for the determinantal varieties with singular set an ICIS.