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Linear Algebra Theory Question - Heisenberg Group

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data

    Let H be the set of all matrices with entries that are integers, with 1s on the main diagonal, and 0s below it.

    A = [1 a b; 0 1 c; 0 0 1]

    Now, if a set of matrices G contains the identity matrix, contains the inverse matrix of every matrix in G, and is closed under matrix multiplication, it is called a matrix group. The group described prior (H) is called the Heisenberg group. Now find the most general matrix C that belongs to H and commutes with all the elements of H, meaning that CA = AC for every A in H.

    2. Relevant equations



    3. The attempt at a solution

    I determined that A^2 and A^-1 still belong to H, but I have no idea how to set this up. Any hints would be greatly appreciated. :)
     
  2. jcsd
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