About: Vector space   Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

A vector space is an algebraic structure consisting of an additive Abelian group (elements of which are called vectors, and are denoted in bold), a field (elements of which are called scalars), and a scalar multiplication function following these properties: As both and each have their own respective additive identites, we will denote boldface to represent the additive identity in . We then say that is a vector space over the field .

AttributesValues
rdfs:label
  • Vector space
rdfs:comment
  • A vector space is an algebraic structure consisting of an additive Abelian group (elements of which are called vectors, and are denoted in bold), a field (elements of which are called scalars), and a scalar multiplication function following these properties: As both and each have their own respective additive identites, we will denote boldface to represent the additive identity in . We then say that is a vector space over the field .
sameAs
dcterms:subject
abstract
  • A vector space is an algebraic structure consisting of an additive Abelian group (elements of which are called vectors, and are denoted in bold), a field (elements of which are called scalars), and a scalar multiplication function following these properties: * Distributive property of scalar multiplication over vector addition: For all and , . * Distributive property of scalar multiplication over field addition: For all and , . * Associative law of combined scalar and field multiplication: For all and , . * Scalar multiplication identity: With 1 as the field multiplicative identity, for all , we have . As both and each have their own respective additive identites, we will denote boldface to represent the additive identity in . We then say that is a vector space over the field .
Alternative Linked Data Views: ODE     Raw Data in: CXML | CSV | RDF ( N-Triples N3/Turtle JSON XML ) | OData ( Atom JSON ) | Microdata ( JSON HTML) | JSON-LD    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3217, on Linux (x86_64-pc-linux-gnu), Standard Edition
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2012 OpenLink Software