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Is there a way to get the determinant $\text{Det}(M)$ of a matrix $M$ from the matrix of its logarithms, i.e.

$\Bigg( \begin{smallmatrix} \log(M_{00}) & \log(M_{01}) & \ldots \\ \log(M_{10}) & \log(M_{11}) & \\ \vdots \end{smallmatrix}\Bigg)\ \ \ \ ? $

Note that I don't mean the actual matrix logarithm; then I could use the second identity in this question.

EDIT: I mean if there is a faster way than exponentiating the elements and computing the determinant from scratch.

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jorgen
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    well, just apply $e^x$ to every entry and compute the determinant of the resulting matrix :) [I guess you want something else, but then you should be more specific] – user8268 Nov 30 '14 at 19:58
  • Haha, good pont:) I'm wondering if there's a faster way to do it, determinant being naively $\mathcal{O}(N^3)$. Wishful thinking..? – jorgen Dec 01 '14 at 02:51

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