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...

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 ∈...

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 )...

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...

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...

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...

{\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...

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)...

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...

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

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...

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...

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

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

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...

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...

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...

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...

set of R-bilinear maps M × N → P and to each R-module homomorphism f : P → Q the function B(f) : B(P) → B(Q) which sends each bilinear map g : M × N...

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...

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...

{\displaystyle p} . A metric tensor is a non-degenerate, smooth, symmetric, bilinear map that assigns a real number to pairs of tangent vectors at each tangent...

{\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...