# Book: ExponentialTraceDeterminant

Give a combinatorial interpretation of the formula:

{$\mathrm{det}(e^A)=e^{\mathrm{tr}(A)}$}

• Give a combinatorial interpretation of {$e^A$}.
• Relate {$\mathrm{tr}(A)$} to the weight lattice.
• Determinant gives the volume. Traces gives?

Note that this is central for the connection between the special linear Lie group (determinant of M is one) and the Lie algebra (trace of A is zero).