About: Dual representation     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : owl:Thing, within Data Space : live.dbpedia.org associated with source document(s)
QRcode icon
http://live.dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FDual_representation

In mathematics, if G is a group and ρ is a linear representation of it on the vector space V, then the dual representation ρ* is defined over the dual vector space V* as follows: ρ*(g) is the transpose of ρ(g−1), that is, ρ*(g) = ρ(g−1)T for all g ∈ G. The dual representation is also known as the contragredient representation. If g is a Lie algebra and π is a representation of it on the vector space V, then the dual representation π* is defined over the dual vector space V* as follows: π*(X) = −π(X)T for all X ∈ g. In both cases, the dual representation is a representation in the usual sense.

AttributesValues
sameAs
foaf:isPrimaryTopicOf
rdfs:comment
  • In mathematics, if G is a group and ρ is a linear representation of it on the vector space V, then the dual representation ρ* is defined over the dual vector space V* as follows: ρ*(g) is the transpose of ρ(g−1), that is, ρ*(g) = ρ(g−1)T for all g ∈ G. The dual representation is also known as the contragredient representation. If g is a Lie algebra and π is a representation of it on the vector space V, then the dual representation π* is defined over the dual vector space V* as follows: π*(X) = −π(X)T for all X ∈ g. In both cases, the dual representation is a representation in the usual sense.
rdfs:label
  • Dual representation
has abstract
  • In mathematics, if G is a group and ρ is a linear representation of it on the vector space V, then the dual representation ρ* is defined over the dual vector space V* as follows: ρ*(g) is the transpose of ρ(g−1), that is, ρ*(g) = ρ(g−1)T for all g ∈ G. The dual representation is also known as the contragredient representation. If g is a Lie algebra and π is a representation of it on the vector space V, then the dual representation π* is defined over the dual vector space V* as follows: π*(X) = −π(X)T for all X ∈ g. The motivation for this definition is that Lie algebra representation associated to the dual of a Lie group representation is computed by the above formula. But the definition of the dual of a Lie algebra representation makes sense even if it does not come from a Lie group representation. In both cases, the dual representation is a representation in the usual sense.
Link to the Wikipage edit URL
extraction datetime
Link to the Wikipage history URL
Wikipage page ID
page length (characters) of wiki page
Wikipage modification datetime
Wiki page out degree
Wikipage revision ID
Link to the Wikipage revision URL
dbp:wikiPageUsesTemplate
dct:subject
is foaf:primaryTopic of
is Wikipage redirect of
Faceted Search & Find service v1.17_git39 as of Aug 10 2019


Alternative Linked Data Documents: iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3319 as of Sep 1 2020, on Linux (x86_64-generic-linux-glibc25), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2021 OpenLink Software