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Adjective:

Bilinear,

bilinear's Usage Examples:

In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each.

mathematics, a bilinear form on a vector space V is a bilinear map V × V → K, where K is the field of scalars.

In other words, a bilinear form is a function.

In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables (e.

defines a bilinear form B : X × X → F, with the relation B(x, y) = u(x)(y).

By defining the transpose of this bilinear form as the bilinear form tB defined.

Quadratic forms correspond one-to-one to symmetric bilinear forms over the same space.

A symmetric bilinear form is also described as definite, semidefinite.

properties may be summarized by saying that the dot product is a bilinear form.

Moreover, this bilinear form is positive definite, which means that a ⋅ a {\displaystyle.

generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space.

A bilinear form is linear in.

numbers R) equipped with a symplectic bilinear form.

A symplectic bilinear form is a mapping ω : V × V → F that is bilinear: linear in each argument separately.

mathematics, specifically linear algebra, a degenerate bilinear form f(x, y) on a vector space V is a bilinear form such that the map from V to V∗ (the dual space.

algebra of bilinear forms.

Two elements u and v of a vector space with bilinear form B are orthogonal when B(u, v) = 0.

Depending on the bilinear form, the.

} Thus, bq is a symmetric bilinear form over K with matrix A.

Conversely, any symmetric bilinear form b defines a quadratic form q ( x ).

field (often simply called an algebra) is a vector space equipped with a bilinear product.

In mathematics, a symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the.

orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W⊥ of all vectors in V that are orthogonal to every vector.

More generally, any bilinear form over a vector space of finite dimension may be expressed as a matrix.

An alternating bilinear form α from Λ to the integers satisfying the following Riemann bilinear relations: the real linear extension.

The bilinear transform (also known as Tustin's method) is used in digital signal processing and discrete-time control theory to transform continuous-time.

upon vectors in the manner of a bilinear map, we will view them instead as objects to be acted upon to produce a bilinear map.

a: System of linear equations, System of nonlinear equations, System of bilinear equations, System of polynomial equations, System of differential equations.

bilinear's Meaning':

linear with respect to each of two variables or positions

Synonyms:

additive; linear;

Antonyms:

nonlinear; subtractive; cubic;