multilinear form
noun1
Linear algebra, Mathematics, Sciences Given a vector space V over a field K of scalars, a mapping Vᵏ → K that is linear in each of its arguments;
Multilinear algebra
- 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.
1 more example
- 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:
› Given a vector space V over a field K of…
2
Linear algebra, Mathematics, Sciences Broadly a similarly multiply linear mapping Mʳ → R defined for a given module M over some commutative ring R.
Multilinear algebra
- Synonyms
- multicovector
- Derived terms
- alternating multilinear form, multilinear k-form
- Related terms
- covariant, differential form, linear, linear form, multilinear algebra, multilinear map, multivector, tensor
- Hyponyms
- bilinear form, covector, linear form