### An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity

Let $(V,0)$ be a germ of a complete intersection variety in ${\u2102}^{n+k}$, $n\>0$, having an isolated singularity at $0$ and $X$ be the germ of a holomorphic vector field having an isolated zero at $0$ and tangent to $V$. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of $X$ is also isolated in the ambient space ${\u2102}^{n+k}$ we give a formula for the homological index in terms of local linear algebra.