Some necessary and some sufficient trace inequalities for Euclidean distance matrices

DOI10.1080/03081080701241570zbMath1129.15015OpenAlexW2087999059MaRDI QIDQ5422403

Abdo Y. Alfakih, Henry Wolkowicz

Publication date: 19 October 2007

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

Full work available at URL: https://doi.org/10.1080/03081080701241570

zbMATH Keywords

smallest eigenvaluetrace inequalities

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Miscellaneous inequalities involving matrices (15A45)

Cites Work

• Bounds for eigenvalues using traces
• Distance matrices and regular figures
• Circum-Euclidean distance matrices and faces
• On the nullspace, the rangespace and the characteristic polynomial of Euclidean distance matrices
• A variance inequality ensuring that a pre-distance matrix is Euclidean
• Remarks to Maurice Frechet's article ``Sur la definition axiomatique d'une classe d'espaces vectoriels distancies applicables vectoriellement sur l'espace de Hilbert

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