In 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...

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

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

linear 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...

Look up multilinear in Wiktionary, the free dictionary. Multilinear may refer to: Multilinear form, a type of mathematical function from a vector space...

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...

multilinear function f : V k → K {\displaystyle f:V^{k}\to K} is called an alternating multilinear form. The set of all alternating multilinear forms...

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

(v_{s})),} which is a multilinear form on V. Hence Φ∗ is a (linear) operator from multilinear forms on W to multilinear forms on V. As a special case...

functional equation and growth condition Multilinear form, which generalises bilinear forms to mappings VN → F Quadratic form, a homogeneous polynomial of degree...

Linear form Multilinear form Polar space Quadratic form Sesquilinear form System of bilinear equations Metric tensor "Chapter 3. Bilinear forms — Lecture...

(k,l)} over M is canonically isomorphic to C∞(M)-module of C∞(M)-multilinear forms Ω 1 ( M ) × … × Ω 1 ( M ) ⏟ l   t i m e s × X ( M ) × … × X ( M )...

differential forms Complex differential form Vector-valued differential form Equivariant differential form Calculus on Manifolds Multilinear form Polynomial...

a topology defined by convex open sets Positive linear functional Multilinear form – Map from multiple vectors to an underlying field of scalars, linear...

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space...

that one can multiply pointwise a k-multilinear form and an l-multilinear form to get a (k + l)-multilinear form. The ring structure in cohomology provides...

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

a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by evaluating along...

representation Monomial matrix Homogeneous polynomial Homogeneous function Multilinear form Log-log plot Power law Sparse polynomial Lang, Serge (2005). Algebra...

non-commutative rings, there is no reasonable notion of a multilinear form (existence of a nonzero bilinear form[clarify] with a regular element of R as value on...

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of...

space of real multilinear maps from VJ to C which are complex linear in p terms and conjugate-linear in q terms. See complex differential form and almost...

views a tensor as an abstract object, expressing some definite type of multilinear concept. Their properties can be derived from their definitions, as linear...

sophisticated settings. Differentiable manifolds Multilinear form The formalisms of differential forms and the exterior calculus used in Calculus on Manifolds...

V\times \cdots \times V\to \mathbf {R} .} This is an n-ary multilinear skew-symmetric form. In the presence of a basis, such as on R n , {\displaystyle...

f:{\mathfrak {g}}\times V\to V} is a multilinear map, φ {\displaystyle \varphi } is a g {\displaystyle {\mathfrak {g}}} -valued form and η {\displaystyle \eta }...

Det(A) = (1/2)εilεjmbijblm. Using the same conventions we can define a multilinear form f(x,y,z) = aijk xiyjzk Then the hyperdeterminant is zero if and only...

Hyperlink cinema is a style of filmmaking characterized by complex or multilinear narrative structures with multiple characters under one unifying theme...

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...

S2CID 29690672. Boneh, Dan; Silverberg, Alice (2002). "Applications of Multilinear Forms to Cryptography". Cryptology ePrint Archive. Dutta, Ratna; Barua,...