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...ote all eigenvalues of ˜ K in a magnitude descending order as {μj} L j=0. We have observed that μ0 > 0 and μj < 0 ∀j > 0. (Such matrix has a single positive eigenvalue, and the rest are negative. See =-=[1]-=- and references therein) Hence a scale invariant spectrum can be defined as ¯μj = ∣ ∣ μj μ0 ∣ . (7) Our shape signature is defined as a vector S =[¯μ1, ¯μ2,...,¯μL] T , which in theory is also isometr...

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...nerating points xi for an EDM matrix D, one can take a look at the singular value decomposition of Gower matrix (1.1) F = − 1 ( T I −es 2 ) D ( I −se T) , where s is a vector such that s T e = 1 (see =-=[1]-=-). Since F is positive semidefinite, it can be written as F = X T X with X = diag( √ σi)U T , where F = UΣU T is the singular value decomposition of F and Σ = diag(σi). The points xi are obtained as c...

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...n. More precisely, in the univariate case, rank(E) ≤ 3, see Lin and Chu [11, Theorem 2.1] for a simple proof. (For more information about EDMs, the interested reader is referred to Gower [6], Alfakih =-=[1]-=-, Krislock and Wolkowicz [9], Li et al. [10], and Jaklic and Modic [7].) The rank deficiency of EDMs has been exploited by Zimmermann [19] in order to establish estimates on the condition number growt...