On the uniqueness of Euclidean distance matrix completions: the case of points in general position

The Euclidean distance matrix completion problem (EDMCP) is the problem of determining whether or not a given partial matrix can be completed into a Euclidean distance matrix (EDM). In this paper, we investigate the necessary and sufficient conditions for the uniqueness of a given EDM completion in the case where this EDM completion is generated by points in general position. We also show that the problem of checking the validity of these conditions can be formulated as a semidefinite programming problem.