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Complex and Real Matrices

  1. Apr 8, 2010 #1
    Let A and B be 2 x 2 real matrices such that A = PBP^-1 for some invertible 2 x 2 complex matrix P. Prove that A = QBQ^-1 for some invertible 2 x 2 real matrix Q.
  2. jcsd
  3. Apr 9, 2010 #2
    A plump calculation shows that Q = PP* ( 8 denotes complex conjugation here).
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