Multilinear Form


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multilinear form

[′məl·tə‚lin·ē·ər ′fȯrm]
(mathematics)
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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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.
Villanueva, Hahn-Banach extension of multilinear forms and summability, J.

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