  The germ of an algebraic variety is naturally equipped with two different
metrics up to bilipschitz equivalence. The inner metric and the outer metric.
One calls a germ of a variety Lipschitz normally embedded if the two metrics
are bilipschitz equivalent. In this article we prove that the model
determinantal singularity, that is the space of $m\times n$ matrices of rank
less than a given number, is Lipschitz normally embedded. We will also discuss
some of the difficulties extending this result to the case of general
determinantal singularities.
