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Jordan Product Properties

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data
    A and B are n x n matrices, so their Jordan Product is (AB + BA)/2. Show that this product is commutative but not associative.


    2. Relevant equations



    3. The attempt at a solution
    I understand the logic behind the answer, but I don't know how to show it. Where would I start?
     
  2. jcsd
  3. Sep 20, 2010 #2
    /edit: deleted answer.

    For associativity, just write out A*B and B*A and expand. For commutivity, write out A*(B*C) and (A*B)*C, and if what you get when you expand the two things is not the same, then you have shown what you wanted.
     
    Last edited: Sep 20, 2010
  4. Sep 20, 2010 #3
    Thank you so much for the help. I figured out this question and the other Jordan Product questions from your advice.
     
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