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symmetric bilinear form (Definition)

A symmetric bilinear form is a bilinear form $ B$ which is symmetric in the two coordinates; that is, $ B(x,y) = B(y,x)$ for all vectors $ x$ and $ y$.

Every inner product over a real vector space is a positive definite symmetric bilinear form.



"symmetric bilinear form" is owned by djao.
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See Also: antisymmetric, quadratic form, skew-symmetric bilinear form

Other names:  symmetric form
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Cross-references: positive definite, vector space, real, inner product, vectors, coordinates, symmetric, bilinear form
There are 22 references to this entry.

This is version 2 of symmetric bilinear form, born on 2002-02-22, modified 2002-04-13.
Object id is 2466, canonical name is SymmetricBilinearForm.
Accessed 6209 times total.

Classification:
AMS MSC11E39 (Number theory :: Forms and linear algebraic groups :: Bilinear and Hermitian forms)
 15A63 (Linear and multilinear algebra; matrix theory :: Quadratic and bilinear forms, inner products)
 47A07 (Operator theory :: General theory of linear operators :: Forms )

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