![]() It is shown that such a decomposition exists for every symmetric matrix and that it is numerically stable. Embedding of a distance matrix yields a decomposition of the associated symmetric matrix in the form of a sum over outer products of a linear independent system of coordinate vectors. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a general distance matrix by a one-to-one transformation. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. ![]() ![]() ![]() A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported.
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