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Matrices and Commutativity

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    (Commutativity) Find all 2 x 2 matrices A = [ajk ] that commute with B = [bjk], where bjk = j+k


    2. Relevant equations



    3. The attempt at a solution
    ajk =
    1,1
    1,1

    bjk =
    j+k, j+k
    j+k, j+k

    I am confused about what they are trying to ask me. I understand that commute means that you can reverse it and you will come out with same outcome. I.E. like 3 x 2 = 6 and 2 x 3 = 6. Can someone give me a clue of what I should try to do.
     
  2. jcsd
  3. Sep 27, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    hmmm... not sure i understand the question, does
    B
    = [bjk] = j + k

    =[b11 b12]
    _[b21 b22]

    =[1+1 1+2]
    _[2+1 2+2]?

    Then to show commutivity, as you implied, you then need to find all matricies A such that
    A.B = B.A = C
    where the C is added to clarify the meaning of the sum below, where the dummy indiceis are summed over
    cik = aij.bjk = bim.amk

    what constraints doe thi put on the values aij
     
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