  We study the equisingularity of a family of function germs
$\{f_t\colon(X_t,0)\to (\mathbb{C},0)\}$, where $(X_t,0)$ are $d$-dimensional
isolated determinantal singularities. We define the $(d-1)$th polar
multiplicity of the fibers $X_t\cap f_t^{-1}(0)$ and we show how the constancy
of the polar multiplicities is related to the constancy of the Milnor number of
$f_t$ and the Whitney equisingularity of the family.
