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Tensor product. . .

  1. Sep 8, 2011 #1
    1. The problem statement, all variables and given/known data
    I don't need help with the main problem, just a calculation: I need to expand out elements of the form [itex](x_i \otimes 1)(1 \otimes x_j)[/itex], etc.

    2. Relevant equations


    3. The attempt at a solution
    Is there a property of the tensor product that I can use to expand out products like the ones above? I have a feeling that I can write [itex](x_i \otimes 1)(1 \otimes x_j) = ((x_i)(1) \otimes (1)(x_j)) = x_i \otimes x_j[/itex], but I'm not 100% sure.\
     
  2. jcsd
  3. Sep 8, 2011 #2

    micromass

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    Yes, that is correct. It follows because multiplication in the tensor product is defined as

    [tex](a\otimes b)(c\otimes d)=ac\otimes bd[/tex]
     
  4. May 10, 2012 #3
    I know this is an old thread, but why tensor product is defined like that? And what do you mean by tensor product in this case?
     
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