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Writing determinant as traces

  1. Dec 2, 2012 #1
    I am reading the paper http://arxiv.org/abs/hep-th/9701037.
    In equation (2), the author write the determinat as traces, but I don't know how to do this.
    I know that ##det(e^A)=e^{tr(A)}##, where ##A## is a complex matrix, and ##det(A)=e^{tr(L)}##, where ##e^L=A## and ##L## is also a complex matrix.
    The problem becomes how to find the logrithm of the matrix ##g_{mn}+i##[itex]\tilde{F}_{mn}[/itex].
    Above is what I can figure out now.

    Any help would be vary appreciated!
    Regards.
     
  2. jcsd
  3. Dec 18, 2012 #2
    You can always post any question you have on math stackexchange .You will get responses more quickly
     
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