About: Euclidean distance matrix     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Matrix108267640, within Data Space : dbpedia.org associated with source document(s)
QRcode icon
http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FEuclidean_distance_matrix&graph=http%3A%2F%2Fdbpedia.org&graph=http%3A%2F%2Fdbpedia.org

In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space.For points in k-dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them.That is where denotes the Euclidean norm on ℝk. In the context of (not necessarily Euclidean) distance matrices, the entries are usually defined directly as distances, not their squares.However, in the Euclidean case, squares of distances are used to avoid computing square roots and to simplify relevant theorems and algorithms.

AttributesValues
rdf:type
rdfs:label
  • Euclidean distance matrix (en)
  • Matrice de distance euclidienne (fr)
rdfs:comment
  • En mathématiques, une matrice de distance euclidienne est une matrice de taille n × n représentant l'espacement d'un ensemble de points dans un espace euclidien. Si l'on note une matrice de distance euclidienne et des points sont définis dans un espace de dimension , alors les éléments de sont donnés par où désigne la norme euclidienne sur . Ainsi, la matrice des distances euclidienne sera de la forme : (fr)
  • In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space.For points in k-dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them.That is where denotes the Euclidean norm on ℝk. In the context of (not necessarily Euclidean) distance matrices, the entries are usually defined directly as distances, not their squares.However, in the Euclidean case, squares of distances are used to avoid computing square roots and to simplify relevant theorems and algorithms. (en)
dcterms:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
Link from a Wikipage to an external page
sameAs
dbp:wikiPageUsesTemplate
has abstract
  • In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space.For points in k-dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them.That is where denotes the Euclidean norm on ℝk. In the context of (not necessarily Euclidean) distance matrices, the entries are usually defined directly as distances, not their squares.However, in the Euclidean case, squares of distances are used to avoid computing square roots and to simplify relevant theorems and algorithms. Euclidean distance matrices are closely related to Gram matrices (matrices of dot products, describing norms of vectors and angles between them).The latter are easily analyzed using methods of linear algebra.This allows to characterize Euclidean distance matrices and recover the points that realize it.A realization, if it exists, is unique up to rigid transformations, i.e. distance-preserving transformations of Euclidean space (rotations, reflections, translations). In practical applications, distances are noisy measurements or come from arbitrary dissimilarity estimates (not necessarily metric).The goal may be to visualize such data by points in Euclidean space whose distance matrix approximates a given dissimilarity matrix as well as possible — this is known as multidimensional scaling.Alternatively, given two sets of data already represented by points in Euclidean space, one may ask how similar they are in shape, that is, how closely can they be related by a distance-preserving transformation — this is Procrustes analysis.Some of the distances may also be missing or come unlabelled (as an unordered set or multiset instead of a matrix), leading to more complex algorithmic tasks, such as the graph realization problem or the turnpike problem (for points on a line). (en)
  • En mathématiques, une matrice de distance euclidienne est une matrice de taille n × n représentant l'espacement d'un ensemble de points dans un espace euclidien. Si l'on note une matrice de distance euclidienne et des points sont définis dans un espace de dimension , alors les éléments de sont donnés par où désigne la norme euclidienne sur . Ainsi, la matrice des distances euclidienne sera de la forme : (fr)
prov:wasDerivedFrom
page length (characters) of wiki page
foaf:isPrimaryTopicOf
is Link from a Wikipage to another Wikipage of
Faceted Search & Find service v1.17_git139 as of Feb 29 2024


Alternative Linked Data Documents: ODE     Content Formats:   [cxml] [csv]     RDF   [text] [turtle] [ld+json] [rdf+json] [rdf+xml]     ODATA   [atom+xml] [odata+json]     Microdata   [microdata+json] [html]    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (62 GB total memory, 40 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software