algebra, a multilinear map is a function of several variables that is linear separately in each variable. More precisely, a multilinear map is a function...

In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same...

vector space to the underlying field Multilinear map, a type of mathematical function between vector spaces Multilinear algebra, a field of mathematics This...

object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects...

A cryptographic n {\displaystyle n} -multilinear map is a kind of multilinear map, that is, a function e : G 1 × ⋯ × G n → G T {\displaystyle e:G_{1}\times...

the proper term is multilinear. For non-commutative rings R and S, a left R-module M and a right S-module N, a bilinear map is a map B : M × N → T with...

abstract algebra and multilinear algebra, a multilinear form on a vector space V {\displaystyle V} over a field K {\displaystyle K} is a map f : V k → K {\displaystyle...

Multilinear algebra is the study of functions with multiple vector-valued arguments, with the functions being linear maps with respect to each argument...

− f ( y , x ) . {\displaystyle f(x,y)=-f(y,x).} More generally, a multilinear map g : A n → B {\displaystyle g:A^{n}\to B} is anticommutative if for...

relies on the yet stronger Decisional Diffie–Hellman (DDH) variant). A multilinear map is a function e : G 1 , … , G n → G T {\displaystyle e:G_{1},\dots...

monomial. Multilinear polynomials can be understood as a multilinear map (specifically, a multilinear form) applied to the vectors [1 x], [1 y], etc. The general...

link Alternating map, a multilinear map that is zero whenever any two of its arguments are equal Alternating operator, a multilinear map in algebra Alternating...

extend the notion of pullback to tensors of arbitrary rank, i.e., to multilinear maps on W taking values in a tensor product of r copies of W, i.e., W ⊗...

associated statistics are called U-statistics. Alternating multilinear map – Multilinear map that is 0 whenever arguments are linearly dependent Antisymmetric...

space. Let S q ( V ) {\displaystyle S^{q}(V)} denote the vector space of multilinear functionals λ : ∏ 1 q V → k {\displaystyle \textstyle \lambda :\prod...

the characterization of the determinant as the unique alternating multilinear map that satisfies det ( I ) = 1 {\displaystyle \det(I)=1} still holds...

ring R in which 2 is not a zero divisor is alternating. Alternating multilinear map Exterior algebra Graded-symmetric algebra Supercommutative algebra...

In multilinear algebra, applying a map that is the tensor product of linear maps to a tensor is called a multilinear multiplication. Let F {\displaystyle...

a multilinear map sp: TpM × TpM → Ep which is completely anti-symmetric. Then the exterior covariant derivative d∇ s assigns to each p a multilinear map...

can be trained. A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects...

subspace Matrix decomposition – Representation of a matrix as a product Multilinear map – Vector-valued function of multiple vectors, linear in each argument...

be a tensor field of type (p, q). Consider T to be a differentiable multilinear map of smooth sections α1, α2, ..., αp of the cotangent bundle T∗M and...

fields!) on M as multilinear maps on vectors and covectors, we can regard general (k,l) tensor fields on M as C∞(M)-multilinear maps defined on k copies...

systems. For a non-associative ring or algebra R, the associator is the multilinear map [ ⋅ , ⋅ , ⋅ ] : R × R × R → R {\displaystyle [\cdot ,\cdot ,\cdot ]:R\times...

∏ i = 1 n X i → Y {\displaystyle M:\prod _{i=1}^{n}X_{i}\to Y} be a multilinear operator that is linear in each of its n {\displaystyle n} coordinates...

form Graded algebra Hilbert series and Hilbert polynomial Multilinear form Multilinear map Polarization of an algebraic form Schur polynomial Symbol of...

anti-symmetric map from two given ones. Suppose ω : Vk → K and η : Vm → K are two anti-symmetric maps. As in the case of tensor products of multilinear maps, the...

Cartesian product of vector spaces on which the tensor is given as a multilinear map V × V × ... × V → R. But equally well defined choices for the divergence...

they are seen as multilinear maps (see also tensors as multilinear maps). Thus the components of the tensor product of multilinear forms can be computed...

universal property of exterior powers, this is equivalently an alternating multilinear map: β p : ⨁ n = 1 k T p M → R . {\displaystyle \beta _{p}\colon \bigoplus...