  Many theoretical results in the machine learning domain stand only for
functions that are Lipschitz continuous. Lipschitz continuity is a strong form
of continuity that linearly bounds the variations of a function. In this paper,
we derive tight Lipschitz constants for two families of metrics: Mahalanobis
distances and bounded-space bilinear forms. To our knowledge, this is the first
time the Mahalanobis distance is formally proved to be Lipschitz continuous and
that such tight Lipschitz constants are derived.
