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det_exp_formula [2013/09/15 21:44] nikolaj |
det_exp_formula [2014/03/21 11:11] (current) |
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| ===== Det exp formula ===== | ===== Det exp formula ===== | ||
| ==== Theorem ==== | ==== Theorem ==== | ||
| - | | @#88DDEE: $ A\in\mathrm{Matrix}(n,\mathbb C) $ | | + | | $ A\in\mathrm{Matrix}(n,\mathbb C) $ | |
| - | | @#55EE55: $\mathrm{det}\left(\mathrm{exp}(A)\right)=\mathrm{e}^{\mathrm{tr}\ A}$ | | + | | @#55EE55: postulate | @#55EE55: $\mathrm{det}\left(\mathrm{exp}(A)\right)=\mathrm{e}^{\mathrm{tr}\ A}$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| + | This is a corollary of Jacobi's formula. | ||
| + | === Reference === | ||
| + | Wikipedia: [[http://en.wikipedia.org/wiki/Jacobi%27s_formula|Jacobi's formula]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| - | [[Determinant]], [[Exponential function]] | + | [[Determinant via multilinear functionals]], [[Exponential function]] |
