DOI: 10.1007/978-3-319-00200-2_7
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Abstract: AbstractWe consider the decision problem asking whether a partial rational symmetric matrix with an all-ones diagonal can be completed to a full positive semidefinite matrix of rank at most k. We show that this problem is N P -hard for any fixed integer k ≥ 2. Equivalently, for k ≥ 2, it is N P -hard to test membership in the rank constrained elliptope E k (G), i.e., the set of all partial matrices with off-diagonal entries specified at the edges of G, that can be completed to a positive semidefinite matrix o…

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