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...

on bilinear maps of topological vector spaces that is weaker than continuity but stronger than separate continuity. Many important bilinear maps that...

In mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements...

In mathematics, a pairing is an R-bilinear map from the Cartesian product of two R-modules, where the underlying ring R is commutative. Let R be a commutative...

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...

alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example, a bilinear form or a multilinear form)...

vector space to which is associated a bilinear map V × W → V ⊗ W {\displaystyle V\times W\rightarrow V\otimes W} that maps a pair ( v , w ) ,   v ∈ V , w ∈...

{\displaystyle 2^{2}} . A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, for any nonnegative...

Look up bilinear in Wiktionary, the free dictionary. Bilinear may refer to: Bilinear sampling (also called "bilinear filtering"), a method in computer...

automatically implies that this bilinear map is induced by a linear functional on V ⊗ V∗. Similarly, there is a natural bilinear map V × V∗ → Hom(V, V) given...

a 1×1 matrix is identified with its unique entry.) More generally, any bilinear form over a vector space of finite dimension may be expressed as a matrix...

Bilinear transformation may refer to: Bilinear map or bilinear operator Bilinear transform (signal processing), a type of conformal map used to switch...

bilinear complexity or rank of a bilinear map is an important concept in the asymptotic complexity of matrix multiplication. The rank of a bilinear map...

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 of V )...

{g}}} together with an operation called the Lie bracket, an alternating bilinear map g × g → g {\displaystyle {\mathfrak {g}}\times {\mathfrak {g}}\rightarrow...

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...

In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It...

it is possible to define the outer product as a linear map V → W. In this case, the linear map x ↦ ⟨ v , x ⟩ {\displaystyle \mathbf {x} \mapsto \langle...

polynomial at i {\displaystyle i} . Why the bilinear map pairing is used The utility of the bilinear map pairing is to allow the multiplication of q (...

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is...

{\displaystyle {\mathbb {G} }_{2}} . There exists an efficiently computable bilinear map (pairing) e ( ⋅ , ⋅ ) : G 1 × G 2 → G T {\displaystyle e(\cdot ,\cdot...

In mathematics, Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory...

Anticommutativity { f , g } = − { g , f } {\displaystyle \{f,g\}=-\{g,f\}} Bilinearity { a f + b g , h } = a { f , h } + b { g , h } , {\displaystyle \{af+bg...

construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms of linear maps. The module construction is analogous...

tensor product of modules, the multiplication (the R-bilinear map) corresponds to a unique R-linear map m : A ⊗ R A → A {\displaystyle m:A\otimes _{R}A\to...

In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. For a vector, v → {\displaystyle...

generally, Young's inequality implies that the convolution is a continuous bilinear map between suitable Lp spaces. Specifically, if 1 ≤ p, q, r ≤ ∞ satisfy:...

In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar. It is often denoted ⟨ A , B ⟩ F {\displaystyle...

{Z} } -bilinear map. Typical examples include maps between rings, vector spaces, or modules that preserve the additive group. An additive map does not...

two arguments. If A , B {\displaystyle A,B} are two abelian groups, a bilinear map f : A 2 → B {\displaystyle f\colon A^{2}\to B} is anticommutative if...