Tensor product of quadratic forms (original) (raw)
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 * e
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| dbo:abstract | 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 * e (en) |
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| dbo:wikiPageWikiLink | dbr:Module_(mathematics) dbr:Bilinear_form dbr:Unit_(ring_theory) dbr:Quadratic_space dbc:Quadratic_forms dbr:Mathematics dbr:Commutative_ring dbr:Quadratic_form dbr:Tensor_product dbr:Tensor_product_of_modules dbc:Tensors dbr:Characteristic_(algebra) |
| dbp:wikiPageUsesTemplate | dbt:Algebra-stub dbt:Unreferenced |
| dcterms:subject | dbc:Quadratic_forms dbc:Tensors |
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| rdfs:comment | 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 * e (en) |
| rdfs:label | Tensor product of quadratic forms (en) |
| owl:sameAs | freebase:Tensor product of quadratic forms yago-res:Tensor product of quadratic forms wikidata:Tensor product of quadratic forms https://global.dbpedia.org/id/4vDR1 |
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