# Writing determinant as traces

by rbwang1225
Tags: determinant, traces, writing
 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##$\tilde{F}_{mn}$. Above is what I can figure out now. Any help would be vary appreciated! Regards.