Multilinear Form

multilinear form [′məl·tə‚lin·ē·ər ′fȯrm]

(mathematics)

A multilinear form of degreenis a polynomial expression which is linear in each ofnvariables.

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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, …, x_n; y₁, y₂, …, y_n; …; u₁, u₂, …, u_n

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).