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