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Multilinear Functions and Polynomials

  1. Jan 15, 2013 #1
    A function [tex]f : \mathbf{R}^n\rightarrow\mathbf{R}[/tex] is multilinear if it's linear in every variable. Is there a multilinear function that's not a multilinear polynomial?

    Given a function defined on the n dimensional hypercube, values of which are 0 or 1, there is a unique multilinear extension to all of R. Is this extension a polynomial?
  2. jcsd
  3. Jan 16, 2013 #2


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    Science Advisor

    No, a "linear function" is a polynomial, by definition, so any multilinear function is a polynomial. Saying "multilinear polynomial" is redundant.
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