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Writing determinant as traces

by rbwang1225
Tags: determinant, traces, writing
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rbwang1225
#1
Dec2-12, 10:25 PM
P: 116
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.
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scottbekerham
#2
Dec18-12, 04:26 AM
P: 49
You can always post any question you have on math stackexchange .You will get responses more quickly


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