Two theorems on Euclidean distance matrices and Gale transform

DOI10.1016/S0024-3795(01)00403-7zbMath1004.15023WikidataQ126789299 ScholiaQ126789299MaRDI QIDQ5956246

Abdo Y. Alfakih, Henry Wolkowicz

Publication date: 28 January 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Euclidean distance matricescorrelation matrixGale transformsemidefinite matrices

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) General theory of distance geometry (51K05) Gale and other diagrams (52B35)

Related Items (12)

A remark on the faces of the cone of Euclidean distance matrices ⋮ On cell matrices: a class of Euclidean distance matrices ⋮ A group majorization ordering for Euclidean distance matrices ⋮ Theory of semidefinite programming for sensor network localization ⋮ LRA: local rigid averaging of stretchable non-rigid shapes ⋮ Characterization of multispherical and block structures of Euclidean distance matrices ⋮ Inverse eigenvalue problem of distance matrix via orthogonal matrix ⋮ Moore-Penrose inverse of a Euclidean distance matrix ⋮ On the nullspace, the rangespace and the characteristic polynomial of Euclidean distance matrices ⋮ On representations of graphs as two-distance sets ⋮ Euclidean Distance Matrices and Applications ⋮ On unit spherical Euclidean distance matrices which differ in one entry

Cites Work

• Properties of Euclidean and non-Euclidean distance matrices
• Remarks to Maurice Frechet's article ``Sur la definition axiomatique d'une classe d'espaces vectoriels distancies applicables vectoriellement sur l'espace de Hilbert
• Geometry of cuts and metrics
• On rigidity and realizability of weighted graphs
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