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Is this a 4-linear form ?

  1. Aug 23, 2007 #1
    Is this a 4-linear form ??

    rather a silly question, but i am a bit confused , could we consider the expression

    [tex] x^{2}-y^{2}+3xy-x^{4}+5y^{4}+ z^{4}-2t^{4}+3xyzt-6x^{2}tz+ 5x^{2}y^{2} [/tex]

    or even in general [tex] A_{i,j}x^{i}x^{j}-Q_{i,j,k,l}x^{i}x^{j}x^{k}x^^{l} [/tex]

    could be considered a 4-linear form??.. i believe this is linear on every argument x^{i} but there seems to be 'mixed up' a 2-from plus a 4-form so i,m not sure what exactly is the proposed object.
  2. jcsd
  3. Aug 23, 2007 #2


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    Science Advisor

    The usual label for such expressions is 4th degree polynomial in 4 variables.
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