On the nonnegative rank of Euclidean distance matrices

Matthew M. Lin; Moody T. Chu

doi:10.1016/j.laa.2010.03.038

On the nonnegative rank of Euclidean distance matrices

Matthew M. Lin, Moody T. Chu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

The Euclidean distance matrix for n distinct points in R^r is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n.

Original language	English
Pages (from-to)	681-689
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	433
Issue number	3
DOIs	https://doi.org/10.1016/j.laa.2010.03.038
Publication status	Published - 2010 Sept 1

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2010.03.038

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title = "On the nonnegative rank of Euclidean distance matrices",

abstract = "The Euclidean distance matrix for n distinct points in Rr is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n.",

author = "Lin, {Matthew M.} and Chu, {Moody T.}",

note = "Funding Information: Corresponding author. E-mail addresses: [email protected] (M.M. Lin), [email protected] (M.T. Chu). 1 This research was supported in part by the National Science Foundation under Grants DMS-0505880 and DMS-0732299. 2 This research was supported in part by the National Science Foundation under Grants DMS-0505880 and DMS-0732299 and NIH Roadmap for Medical Research Grant 1 P20 HG003900-01.",

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AU - Chu, Moody T.

N1 - Funding Information: Corresponding author. E-mail addresses: [email protected] (M.M. Lin), [email protected] (M.T. Chu). 1 This research was supported in part by the National Science Foundation under Grants DMS-0505880 and DMS-0732299. 2 This research was supported in part by the National Science Foundation under Grants DMS-0505880 and DMS-0732299 and NIH Roadmap for Medical Research Grant 1 P20 HG003900-01.

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N2 - The Euclidean distance matrix for n distinct points in Rr is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n.

AB - The Euclidean distance matrix for n distinct points in Rr is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n.

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On the nonnegative rank of Euclidean distance matrices

Abstract

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