The $n$ Body Matrix and Its Determinant

DOI10.1137/18M1175410zbMath1442.70008arXiv1802.02900MaRDI QIDQ5742689

Darij Grinberg, Peter J. Olver

Publication date: 8 May 2019

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.02900

zbMATH Keywords

distance geometrydeterminant\(n\) body problemCayley-Menger matrix\(n\) body matrixeuclidean distance matrix

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) General theory of distance geometry (51K05) (n)-body problems (70F10)

Related Items (3)

Invariants of finite and discrete group actions via moving frames ⋮ Polynomial-Time Algorithms for Continuous Metrics on Atomic Clouds of Unordered Points ⋮ A double Sylvester determinant

Cites Work

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• Invariant theory, Young bitableaux, and combinatorics
• Irreducibility of the Cayley-Menger determinant and of a class of related polynomials
• Remarks to Maurice Frechet's article ``Sur la definition axiomatique d'une classe d'espaces vectoriels distancies applicables vectoriellement sur l'espace de Hilbert
• New Foundation of Euclidean Geometry
• The quantumn-body problem in dimensiond⩾n– 1: ground state
• Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability
• Applied Linear Algebra
• Undergraduate Convexity
• Euclidean Distance Geometry
• Three-body problem in 3D space: ground state, (quasi)-exact-solvability
• Joint invariant signatures

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