bilinear form

a function or functional of two variables that is linear with respect to each variable when the other variable is held fixed.

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Universalium. 2010.

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  • Bilinear form — In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F , where F is the field of scalars. That is, a bilinear form is a function B : V × V → F which is linear in each argument separately::egin{array}{l} ext{1. }B(u + …   Wikipedia

  • bilinear form — Math. a function or functional of two variables that is linear with respect to each variable when the other variable is held fixed. [1965 70] …   Useful english dictionary

  • Symmetric bilinear form — A symmetric bilinear form is, as the name implies, a bilinear form on a vector space that is symmetric. They are of great importance in the study of orthogonal polarities and quadrics.They are also more briefly referred to as symmetric forms when …   Wikipedia

  • Definite bilinear form — In mathematics, a definite bilinear form is a bilinear form B over some vector space V (with real or complex scalar field) such that the associated quadratic form is definite, that is, has a real value with the same sign (positive or negative)… …   Wikipedia

  • Strongly positive bilinear form — A bilinear form, a (•,•), is a strongly positive bilinear form if and only if there exists a constant, c >0, such that : a(u,u) geq c cdot |u|^2 .References* AMS 108 p.120 …   Wikipedia

  • Bilinear — may refer to* Bilinear sampling, a method in computer graphics for choosing the color of a texture. * Bilinear form * Bilinear interpolation * Bilinear map, a type of mathematical function between vector spaces * Bilinear transform, a method of… …   Wikipedia

  • Form — may mean: *Form, the shape, appearance, or configuration, of an object *Form (furniture), a long seat or bench without a back *Form (education), a class, set or group of students *Form, a shallow depression or flattened nest of grass used by a… …   Wikipedia

  • Bilinear map — In mathematics, a bilinear map is a function of two arguments that is linear in each. An example of such a map is multiplication of integers.DefinitionLet V , W and X be three vector spaces over the same base field F . A bilinear map is a… …   Wikipedia

  • form — I. noun Etymology: Middle English forme, from Anglo French furme, forme, from Latin forma form, beauty Date: 13th century 1. a. the shape and structure of something as distinguished from its material b. a body (as of a person) especially in its… …   New Collegiate Dictionary

  • Bilinear interpolation — In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables on a regular grid. The key idea is to perform linear interpolation first in one direction, and then again in the other… …   Wikipedia

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