Multilinear Form

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multilinear form

[′məl·tə‚lin·ē·ər ′fȯrm]
A multilinear form of degree n is a polynomial expression which is linear in each of n variables.

Multilinear Form


an algebraic expression of the form

This expression is a polynomial containing m sets of variables, with n variables in each set:

x1, x2, …, xn; y1, y2, …, yn; …; u1, u2, …, un

Each term of the polynomial is of the first degree in a variable from each set. A multilinear form is thus a linear polynomial expression in the variables of one set—hence its name. Special types of multilinear forms include the linear form (m = 1)

the bilinear form (m = 2)

and the trilinear form (m = 3).

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References in periodicals archive ?
We consider the multilinear form of the utility function and show the results for a two-attribute problem, although the result is generalizable for more attributes using the same principles.
In representing the transnational networks of globalization, network films develop a multilinear form in which seemingly unrelated plots and protagonists are brought together by various means.
The most simple model of the relation between images and CGRs (usually taken as log(v)) may be expressed in a multilinear form (Lauschmann et al., 2002)
By using the alternation multilinear form, we can rewrite the elements from the wedge notation into tensor product by taking into account the signs of the permutations, so
Seeger, Smart, and Street introduce a class of multilinear singular integral forms that generalize the Christ-Journe multilinear forms. The research is partially motivated by an approach to Bressan's problems on incompressible mixing flows, they say, and a key aspect of the theory is that the class of operators is closed under adjoints, that is, the class of multilinear forms is closed under permutations of the entries.
Praciano-Pereira, On bounded multilinear forms on a class of [l.sup.p] spaces, J.
Maxwell's equations are derived by considering the canonical differential forms representing alternating multilinear forms which are obtained from the standard representation by the Hodge star operator.
Han, "Perron-Frobenius theorem for nonnegative multilinear forms and extensions," Linear Algebra and its Applications, vol.

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