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Matrix Power Question

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data
    For what positive integers x and n is there a real nxn matrix whose d-th power is -I (negative identity matrix)

    2. Relevant equations

    3. The attempt at a solution

    I don't really understand this problem, aren't there endless possibilities? Also, why does it matter what size the matrix is? :confused:
  2. jcsd
  3. Feb 18, 2009 #2


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    What's this mysterious integer x? Is it the same as d?
  4. Feb 19, 2009 #3
    Yeah sorry that's supposed to be a d. I'm assuming there is a solution to this other than the negative identity matrix?
  5. Feb 19, 2009 #4


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    Well, yes, e.g. A=[[0,1],[-1,0]] is a 2x2 matrix and A^2=-I.
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