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det_exp_formula [2013/09/19 21:10] nikolaj |
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| - | ===== Det exp formula ===== | ||
| - | ==== Theorem ==== | ||
| - | | $ A\in\mathrm{Matrix}(n,\mathbb C) $ | | ||
| - | | @#55EE55: $\mathrm{det}\left(\mathrm{exp}(A)\right)=\mathrm{e}^{\mathrm{tr}\ A}$ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | This is a corollary of Jacobi's formula. | ||
| - | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Jacobi%27s_formula|Jacobi's formula]] | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Determinant via multilinear functionals]], [[Exponential function]] | ||
