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Given a vector space V over a field K of scalars, a mapping Vk → K that is linear in each of its arguments;
Definition source: English Wiktionary via Wiktextract
Qualifier: multilinear algebra
Topics: linear-algebra, mathematics, sciences
Examples
- 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.
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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.
Definition source: English Wiktionary via Wiktextract
Usage: broadly
Qualifier: multilinear algebra
Topics: linear-algebra, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
4 source translations are retained for this English entry.
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French:
forme multilinéaire
— multiply linear mapping to a field of scalars
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German:
Multilinearform
— multiply linear mapping to a field of scalars
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Spanish:
forma multilineal
— multiply linear mapping to a field of scalars
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Spanish:
función multilineal
— multiply linear mapping to a field of scalars
