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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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).

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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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.

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