PlanetMath: non-degenerate bilinear form

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non-degenerate bilinear form

(Definition)

A bilinear form over a vector space is said to be non-degenerate when

if $B({{\bf x}},{{\bf y}}) = 0$ for all ${{\bf x}} \in V$ , then ${{\bf y}} = {{\bf0}}$ , and
if $B({{\bf x}},{{\bf y}}) = 0$ for all ${{\bf y}} \in V$ , then ${{\bf x}} = {{\bf0}}$ .

"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 41 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 14993 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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