Equality relating Euclidean distance cone to positive semidefinite cone

Linear Algebra and Its Applications

Volumn 428, Issue 11-12, 2008, Pages 2597-2600

  Dattorro, Jon ^a  

^a NONE

Author keywords

15A48; 51K05; 52A20; 74P20; 90C25; Distance matrix

Indexed keywords

LINEAR ALGEBRA;

15A48; 52A20; 74P20; DISTANCE MATRIX;

METRIC SYSTEM; MATRIX ALGEBRA;

DISTANCE MATRICES; EUCLIDEAN DISTANCE; EUCLIDEAN DISTANCE MATRICES; KNOW-THAT; POSITIVE SEMIDEFINITE; POSITIVE SEMIDEFINITE MATRICES; SYMMETRIC MATRICES;

EID: 41549152026     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2007.12.008     Document Type: Article

References (8)

1. Frank Critchley. Multidimensional Scaling: A Critical Examination and Some New Proposals. Ph.D. thesis, University of Oxford, Nuffield College, 1980.
2. Critchley F. On certain linear mappings between inner-product and squared-distance matrices. Linear Algebra Appl. 105 (1988) 91-107
3. Deutsch F. Best Approximation in Inner Product Spaces (2001), Springer-Verlag
4. Gaffke N., and Mathar R. A cyclic projection algorithm via duality. Metrika 36 (1989) 29-54
5. Hayden T.L., Wells J., Liu W.-M., and Tarazaga P. The cone of distance matrices. Linear Algebra Appl. 144 (1991) 153-169
6. Laurent M. A tour d'horizon on positive semidefinite and Euclidean distance matrix completion problems. In: Pardalos P.M., and Wolkowicz H. (Eds). Topics in Semidefinite and Interior-Point Methods (1998), American Mathematical Society 51-76
7. Moreau J.-J. Décomposition orthogonale d'un espace Hilbertien selon deux cônes mutuellement polaires. Comptes Rendus de l'Académie des Sciences, Paris 255 (1962) 238-240
8. Schoenberg I.J. Remarks to Maurice Fréchet's article "Sur la définition axiomatique d'une classe d'espace distanciés vectoriellement applicable sur l'espace de Hilbert". Annals of Mathematics 36 3 (1935) 724-732