http://dbpedia.org/ontology/abstract
|
In algebra, a polynomial map or polynomial … In algebra, a polynomial map or polynomial mapping between vector spaces over an infinite field k is a polynomial in linear functionals with coefficients in k; i.e., it can be written as where the are linear functionals and the are vectors in W. For example, if , then a polynomial mapping can be expressed as where the are (scalar-valued) polynomial functions on V. (The abstract definition has an advantage that the map is manifestly free of a choice of basis.) When V, W are finite-dimensional vector spaces and are viewed as algebraic varieties, then a polynomial mapping is precisely a morphism of algebraic varieties. One fundamental outstanding question regarding polynomial mappings is the Jacobian conjecture, which concerns the sufficiency of a polynomial mapping to be invertible. of a polynomial mapping to be invertible.
|
http://dbpedia.org/ontology/wikiPageID
|
56059449
|
http://dbpedia.org/ontology/wikiPageLength
|
1488
|
http://dbpedia.org/ontology/wikiPageRevisionID
|
1092182206
|
http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Polynomial_function +
, http://dbpedia.org/resource/Claudio_Procesi +
, http://dbpedia.org/resource/Abstract_algebra +
, http://dbpedia.org/resource/Field_%28mathematics%29 +
, http://dbpedia.org/resource/Category:Algebra +
, http://dbpedia.org/resource/Jacobian_conjecture +
, http://dbpedia.org/resource/Linear_functional +
, http://dbpedia.org/resource/Polynomial +
, http://dbpedia.org/resource/Polynomial_functor +
, http://dbpedia.org/resource/Vector_space +
, http://dbpedia.org/resource/Morphism_of_algebraic_varieties +
, http://dbpedia.org/resource/Algebraic_varieties +
, http://dbpedia.org/resource/Dimension_%28vector_space%29 +
|
http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Short_description +
, http://dbpedia.org/resource/Template:Isbn +
, http://dbpedia.org/resource/Template:Algebra-stub +
|
http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Algebra +
|
http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Polynomial_mapping?oldid=1092182206&ns=0 +
|
http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Polynomial_mapping +
|
owl:sameAs |
https://global.dbpedia.org/id/4Y6Ma +
, http://www.wikidata.org/entity/Q48970625 +
, http://dbpedia.org/resource/Polynomial_mapping +
|
rdfs:comment |
In algebra, a polynomial map or polynomial … In algebra, a polynomial map or polynomial mapping between vector spaces over an infinite field k is a polynomial in linear functionals with coefficients in k; i.e., it can be written as where the are linear functionals and the are vectors in W. For example, if , then a polynomial mapping can be expressed as where the are (scalar-valued) polynomial functions on V. (The abstract definition has an advantage that the map is manifestly free of a choice of basis.) is manifestly free of a choice of basis.)
|
rdfs:label |
Polynomial mapping
|