1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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 =

    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


    User Avatar
    Homework Helper

    hmmm... not sure i understand the question, does
    = [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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook