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Basic matrix multiplication

  1. Feb 19, 2014 #1
    1. The problem statement, all variables and given/known data
    This isn't homework, but I didn't know where else to ask and I have a test in an hour and a half. The study guide says be able to explain why statements like (A+B)^2 = A^2 + 2AB + B^2 are bogus when dealing with matrix's. Is it because (A+B) = (B+A) but (A+B)^2 /= (B+A)^2 or something? Thx in advance


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 19, 2014 #2

    tiny-tim

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    Hi PsychonautQQ! :wink:

    In any algebra, you can use the distributive law.

    So (A + B)(A + B) = AA + BB + AB + BA.

    Sooo … ? :smile:
     
  4. Feb 19, 2014 #3
    well in matrix multiplaction, AB /= BA.. so in that regard it differs from normal algebra. My study guide says "Be able to explain why statements like (A+B)^2 = A^2 + 2AB + B^2 are nonsense.. and you are saying it's not nonsense? o_O
    conflicted ;-/
     
  5. Feb 19, 2014 #4

    HallsofIvy

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    The crucial point is that matrix multiplication is NOT commutative. That is, in general, AB is NOT equal to BA so in tiny-tim's calculation, (A+ B)(A+ B)= AA+ BB+ AB+ BA is NOT equal to [tex]A^2+ B^2+ AB+ AB= A^2+ B^2+ 2AB[/tex].
     
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