Bilinear map information

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...

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...

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 )...

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 ∈...

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

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

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)...

{\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...

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...

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} )...

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

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...

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...

anti-symmetric map is its double. The symmetrization and antisymmetrization of a bilinear map are bilinear; thus away from 2, every bilinear form is a sum...

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

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...

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

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...

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

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...

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

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

separately continuous bilinear maps and B ( X , Y ; Z ) {\displaystyle B(X,Y;Z)} denote the space of continuous bilinear maps, where X , Y , {\displaystyle...

{\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...