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non-degenerate bilinear form
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(Definition)
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A bilinear form $B$ over a vector space $V$ is said to be non-degenerate when
- if $B({{\bf x}},{{\bf y}}) = 0$ for all ${{\bf x}} \in V$ then ${{\bf y}} = {{\bf 0}}$ and
- if $B({{\bf x}},{{\bf y}}) = 0$ for all ${{\bf y}} \in V$ then ${{\bf x}} = {{\bf 0}}$
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"non-degenerate bilinear form" is owned by djao.
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| Other names: |
non-degenerate form, nondegenerate bilinear form, nondegenerate form, non-degenerate, nondegenerate |
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Cross-references: vector space, bilinear form
There are 42 references to this entry.
This is version 2 of non-degenerate bilinear form, born on 2002-02-22, modified 2005-05-10.
Object id is 2483, canonical name is NonDegenerateBilinearForm.
Accessed 17954 times total.
Classification:
| AMS MSC: | 11E39 (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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Pending Errata and Addenda
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