Dictionary

multilinear form en · NOUN

Meanings

1. (qualifier:multilinear algebra) Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;
   • 1994, Hessam Khoshnevisan, Mohamad Afshar, Mechanical Elimination of Commutative Redundancy, Baudouin Le Charlier (editor), Static Analysis: 1st International Static Analysis Symposium, Proceedings, Volume 1, Springer, LNCS 864, page 454, A multilinear form is said to be degenerate if all its function variables are identical. Thus a degenerate m-multilinear form can more concisely be written as M!f.
   • 1985, Jack Peetre, Paracommutators and Minimal Spaces, S. C. Power (editor) Operators and Function Theory, Kluwer Academic (D. Reidel), page 163, Finally, in the short Lecture 5 we make some remarks on multilinear forms over Hilbert spaces, a theory which is still in a rather embryonic state, motivated by the observation that paracommutators (and Hankel operators too) really should be viewed as forms, not operators.
   • Since the coordinates of a vector change in transforming to a new basis, the same is true of the coefficients of a multilinear form (since the form itself is to remain invariant). 2003, Maks A. Akivis, Vladislav V. Goldberg, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 55:
2. (broadly, qualifier:multilinear algebra) Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments; (more generally) a similarly multiply linear mapping Mʳ → R defined for a given module M over some commutative ring R. ▸ a similarly multiply linear mapping Mʳ → R defined for a given module M over some commutative ring R.

Forms

Deriveds

alternating multilinear form · multilinear k-form

Hyponyms

covector (multiply linear mapping to a field of scalars) · bilinear form (multiply linear mapping to a field of scalars) · linear form (multiply linear mapping to a field of scalars)

Relateds

linear form · differential form · tensor · multilinear algebra · multilinear map · multivector · linear · covariant

Synonyms

multicovector (multiply linear mapping to a field of scalars)

Translations (4)

es forma multilineal (multiply linear mapping to a field of scalars) · de Multilinearform (multiply linear mapping to a field of scalars) · es función multilineal (multiply linear mapping to a field of scalars) · fr forme multilinéaire (multiply linear mapping to a field of scalars)