# 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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