On the nonnegative rank of Euclidean distance matrices

Linear Algebra and Its Applications

Volumn 433, Issue 3, 2010, Pages 681-689

  Lin, Matthew M ^a   Chu, Moody T ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Euclidean distance matrix; Nonnegative rank; Nonnegative rank factorization

Indexed keywords

DISTINCT POINTS; EUCLIDEAN DISTANCE MATRICES; EUCLIDEAN DISTANCE MATRIX; GEOMETRIC ARGUMENTS;

FACTORIZATION; SPATIAL VARIABLES MEASUREMENT;

MATRIX ALGEBRA;

EID: 77953135527     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2010.03.038     Document Type: Article

References (18)

1. Beasley L.B., and Laffey T.J. Real rank versus nonnegative rank. Linear Algebra Appl. 431 (2009) 2330-2335
2. Berman A., and Plemmons R.J. Matrix group monotonicity. Proc. Amer. Math. Soc. 46 (1974) 355-359
3. Berman A., and Plemmons R.J. Nonnegative matrices in the mathematical sciences. Classics in Applied Mathematics vol. 9 (1994), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA Revised reprint of the 1979 original
4. Campbell S.L., and Poole G.D. Computing nonnegative rank factorizations. Linear Algebra Appl. 35 (1981) 175-182
5. Chu M.T., and Lin M.M. Low-dimensional polytope approximation and its applications to nonnegative matrix factorization. SIAM J. Sci. Comput. 30 (2008) 1131-1155
6. Cohen J.E., and Rothblum U.G. Nonnegative ranks, decompositions, and factorizations of nonnegative matrices. Linear Algebra Appl. 190 (1993) 149-168
7. Crippen G.M., and Havel T.F. Distance geometry and molecular conformation. Chemometrics Series vol. 15 (1988), Research Studies Press Ltd., Chichester
8. J. Dattorro, Euclidean distance matrix, Thesis, Stanford University, 2004. .
9. Glunt W., Hayden T.L., and Raydan M. Molecular conformations from distance matrices. J. Comput. Chem. 14 (1993) 114-120
10. Gower J.C. Euclidean distance geometry. Math. Sci. 7 (1982) 1-14
11. † A ≥ 0. Linear and Multilinear Algebra 51 (2003) 83-95
12. Jeter M.W., and Pye W.C. A note on nonnegative rank factorizations. Linear Algebra Appl. 38 (1981) 171-173
13. Jeter M.W., and Pye W.C. Some nonnegative matrices without nonnegative rank factorizations. Indust. Math. 32 (1982) 37-41
14. Klain D.A., and Rota G.-C. Introduction to Geometric Probability, Lezioni Lincee [Lincei Lectures] (1997), Cambridge University Press, Cambridge
15. Richman D.J., and Schneider H. Primes in the semigroup of non-negative matrices. Linear and Multilinear Algebra 2 (1974) 135-140
16. J.J. Sylvester, On a special class of questions on the theory of probabilities, Birmingham British Assoc. Rept., 1865, pp. 8-9.
17. Thomas L.B. Solution to problem 73-14: rank factorization of nonnegative matrices by a. berman and r. j. plemmons. SIAM Rev. 16 (1974) 393-394
18. S.A. Vavasis, On the complexity of nonnegative matrix factorization, 2007. Available at .