In this thesis we adress the problem of distance matrix completions. The goal is to determine all distances or unknown elements in a partial matrix with data on the distances between points. We prove a sufficient condition for the existence of a distance matrix completion and derive conditions for its uniqueness. We present a numerical algorithm that returns a distance matrix completion when the sufficient condition is met. Additionally, we present the problem of finding a distance matrix completion where the sufficient condition is not met, but we know that a completion exists.
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