Definition:Bilinear Form
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space
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This page is about Bilinear Form. For other uses, see Bilinear Mapping.
Definition
Let $R$ be a ring.
Let $M$ be an $R$-module.
A bilinear form on $M$ is a bilinear mapping $b : M \times M \to R$.
In the context of calculus of variations
Let $B$ be a bilinear functional.
Let $B$ be defined on a finite-dimensional space.
Then $B$ is a bilinear form.
space
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Also see
- Definition:Relative Matrix of Bilinear Form
- Definition:Quadratic Form
- Definition:Associated Quadratic Form
- Definition:Bilinear Space
Sources
- 1963: I.M. Gelfand and S.V. Fomin: Calculus of Variations ... (previous) ... (next): $\S 5.24$: Quadratic Functionals. The Second Variation of a Functional
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: bilinear
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: bilinear