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Maximum of trace

  1. Feb 3, 2006 #1
    Assume [tex] A [/tex] is a complex [tex] N \times N [/tex] matrix. It is well known that [tex] \max_{V \in U(N)} |Tr(AV)| = Tr(\sqrt{AA^{\dagger}})[/tex]. But what is
    [tex] \max_{V \in U(N)} Re(Tr(AV)) [/tex]?

    [tex] U(N) [/tex] is the group of unitary [tex] N \times N [/tex] matrices.

    (I could not preview my post properly, so I apologize for any latex-misstakes )
    Last edited: Feb 3, 2006
  2. jcsd
  3. Feb 3, 2006 #2
    You may ignore this question. It was not very difficult to show that [tex] \max_{V \in U(N)} Re(Tr(AV))=Tr(\sqrt{AA^{\dagger}})[/tex] aswell. :blushing:
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