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...

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

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

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...

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...

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...

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...

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 ⊗...

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...

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

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...

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...

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...

∏ 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...

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...

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...

the vector space V* consisting of linear maps f : V → F where F is the field of scalars. Multilinear maps T : Vn → F can be described via tensor products...

(2016). "An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero". LMS Journal of Computation and...

map as the sum of rank-one linear maps. As such, the proof may be written in the notation of tensor products. Then one may consider the multilinear map...

and for each x ∈ U {\displaystyle x\in U} there exists a continuous multilinear map A {\displaystyle A} of n + 1 {\displaystyle n+1} arguments such that...

strict versions of multilinear maps, constructing a candidate based on maps of degree up to 30, and eventually a candidate based on maps of degree up to...

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...

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

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...

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...

sense. If one views the permanent as a map that takes n vectors as arguments, then it is a multilinear map and it is symmetric (meaning that any order...

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