| http://dbpedia.org/ontology/abstract
|
In mathematics, the tensor product of quad … In mathematics, the tensor product of quadratic forms is most easily understood when one views the quadratic forms as quadratic spaces. If R is a commutative ring where 2 is invertible (that is, R has characteristic ), and if and are two quadratic spaces over R, then their tensor product is the quadratic space whose underlying R-module is the tensor product of R-modules and whose quadratic form is the quadratic form associated to the tensor product of the bilinear forms associated to and . In particular, the form satisfies (which does uniquely characterize it however). It follows from this that if the quadratic forms are diagonalizable (which is always possible if 2 is invertible in R), i.e., then the tensor product has diagonalization
* v
* t
* eproduct has diagonalization
* v
* t
* e
|
| http://dbpedia.org/ontology/wikiPageID
|
10137896
|
| http://dbpedia.org/ontology/wikiPageLength
|
1591
|
| http://dbpedia.org/ontology/wikiPageRevisionID
|
1010468815
|
| http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Mathematics +
, http://dbpedia.org/resource/Unit_%28ring_theory%29 +
, http://dbpedia.org/resource/Module_%28mathematics%29 +
, http://dbpedia.org/resource/Commutative_ring +
, http://dbpedia.org/resource/Quadratic_form +
, http://dbpedia.org/resource/Category:Tensors +
, http://dbpedia.org/resource/Characteristic_%28algebra%29 +
, http://dbpedia.org/resource/Bilinear_form +
, http://dbpedia.org/resource/Tensor_product +
, http://dbpedia.org/resource/Category:Quadratic_forms +
, http://dbpedia.org/resource/Quadratic_space +
, http://dbpedia.org/resource/Tensor_product_of_modules +
|
| http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Algebra-stub +
, http://dbpedia.org/resource/Template:Unreferenced +
|
| http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Tensors +
, http://dbpedia.org/resource/Category:Quadratic_forms +
|
| http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Tensor_product_of_quadratic_forms?oldid=1010468815&ns=0 +
|
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Tensor_product_of_quadratic_forms +
|
| owl:sameAs |
http://dbpedia.org/resource/Tensor_product_of_quadratic_forms +
, https://global.dbpedia.org/id/4vDR1 +
, http://rdf.freebase.com/ns/m.02q307p +
, http://www.wikidata.org/entity/Q7700715 +
, http://yago-knowledge.org/resource/Tensor_product_of_quadratic_forms +
|
| rdf:type |
http://dbpedia.org/class/yago/Part113809207 +
, http://dbpedia.org/class/yago/Relation100031921 +
, http://dbpedia.org/class/yago/Form106290637 +
, http://dbpedia.org/class/yago/Abstraction100002137 +
, http://dbpedia.org/class/yago/Variable105857459 +
, http://dbpedia.org/class/yago/LanguageUnit106284225 +
, http://dbpedia.org/class/yago/Cognition100023271 +
, http://dbpedia.org/class/yago/Idea105833840 +
, http://dbpedia.org/class/yago/Content105809192 +
, http://dbpedia.org/class/yago/WikicatTensors +
, http://dbpedia.org/class/yago/Quantity105855125 +
, http://dbpedia.org/class/yago/Tensor105864481 +
, http://dbpedia.org/class/yago/WikicatQuadraticForms +
, http://dbpedia.org/class/yago/Word106286395 +
, http://dbpedia.org/class/yago/PsychologicalFeature100023100 +
, http://dbpedia.org/class/yago/Concept105835747 +
|
| rdfs:comment |
In mathematics, the tensor product of quad … In mathematics, the tensor product of quadratic forms is most easily understood when one views the quadratic forms as quadratic spaces. If R is a commutative ring where 2 is invertible (that is, R has characteristic ), and if and are two quadratic spaces over R, then their tensor product is the quadratic space whose underlying R-module is the tensor product of R-modules and whose quadratic form is the quadratic form associated to the tensor product of the bilinear forms associated to and . In particular, the form satisfies then the tensor product has diagonalization
* v
* t
* eproduct has diagonalization
* v
* t
* e
|
| rdfs:label |
Tensor product of quadratic forms
|
