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...

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...

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

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 )...

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...

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 ∈...

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

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

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...

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...

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...

{\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...

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

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)...

product can be seen as the (1,2)-tensor (a mixed tensor, specifically a bilinear map) obtained from the 3-dimensional volume form, a (0,3)-tensor, by raising...

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...

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

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...

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...

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

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

a bijection. The set of continuous linear maps X → Z {\displaystyle X\to Z} (resp. continuous bilinear maps X × Y → Z {\displaystyle X\times Y\to Z} )...

An integral bilinear form is a bilinear functional that belongs to the continuous dual space of X ⊗ ^ ϵ Y {\displaystyle X{\widehat {\otimes }}_{\epsilon...

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...

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...

nondegenerate bilinear forms BX and BY, a concept known as the adjoint, which is closely related to the transpose, may be defined: If u : X → Y is a linear map between...

{\displaystyle Q(av)=a^{2}Q(v).} When the characteristic of K is not 2, the bilinear map B : V × V → K over K is defined: B ( v , w ) = 1 2 ( Q ( v + w ) − Q...

Such a rule will hold for any continuous bilinear product operation. Let B : X × Y → Z be a continuous bilinear map between vector spaces, and let f and g...

we have), C ∞ ( M ) {\displaystyle C^{\infty }(M)} is equipped with a bilinear map called the Poisson superbracket turning it into a Poisson superalgebra...