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Derived eigenvalues of symmetric matrices, with applications to distance geometry. (English) Zbl 0706.15009
Let \(A\in R^{n\times n}\) and j be the all-one vector of dimension n. The derived eigenvalues of the symmetric matrix A are the zeros of \(P_ A(s)=-j^ Tadj (Is-A)j\). With this notion a new characterization for the embeddability of a finite metric space into Euclidean space is given. In more detail the particular case of two-distance sets is discussed.
Reviewer: M.Voicu

15A18 Eigenvalues, singular values, and eigenvectors
51K05 General theory of distance geometry
15B57 Hermitian, skew-Hermitian, and related matrices
Full Text: DOI
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