See multilinear form on Wiktionary
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"word": "alternating multilinear form"
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"text": "1985, Jack Peetre, Paracommutators and Minimal Spaces, S. C. Power (editor) Operators and Function Theory, Kluwer Academic (D. Reidel), page 163,\nFinally, 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."
},
{
"text": "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,\nA 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."
},
{
"ref": "2003, Maks A. Akivis, Vladislav V. Goldberg, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 55:",
"text": "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).",
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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;"
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"(linear algebra, 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;"
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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;\n(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."
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"text": "1985, Jack Peetre, Paracommutators and Minimal Spaces, S. C. Power (editor) Operators and Function Theory, Kluwer Academic (D. Reidel), page 163,\nFinally, 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."
},
{
"text": "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,\nA 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."
},
{
"ref": "2003, Maks A. Akivis, Vladislav V. Goldberg, translated by Vladislav V. Goldberg, Tensor Calculus with Applications, World Scientific, page 55:",
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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;\n(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."
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Download raw JSONL data for multilinear form meaning in All languages combined (4.6kB)
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