1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Science Advisor

    No, a "linear function" is a polynomial, by definition, so any multilinear function is a polynomial. Saying "multilinear polynomial" is redundant.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook