Converting a distance matrix into Euclidean vector

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I have a distance matrix between different elements. Now I want to calculate the Euclidean vectors that have resulted in that matrix. Is there any efficient method that can do so?

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Distance matrices only give the pairwise distances within a finite set of points. The positions of at least three points must be known for the distance matrix to be enough to determine the positio0ns of the others as vectors from the origin. Given three known points, any other point is at the intersection of the circles with centre one of the three points and radius the distance from that point.