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matrix_exponential [2014/01/29 19:41] nikolaj |
matrix_exponential [2014/03/21 11:11] |
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| - | ===== Matrix exponential ===== | ||
| - | ==== Set ==== | ||
| - | | @#88DDEE: $ n\in\mathbb N $ | | ||
| - | | @#FFBB00: $\mathrm{exp}: \text{SquareMatrix}(n,\mathbb C)\to\text{SquareMatrix}(n,\mathbb C)$ | | ||
| - | | @#FFBB00: $\mathrm{exp}(A):=\sum_{k=0}^\infty \frac{1}{k!} A^k $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | === Theorems === | ||
| - | ^ $[A,B]=0\implies \mathrm{exp}(A+B)=\mathrm{exp}(A)\mathrm{exp}(B)$ ^ | ||
| - | === References === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Matrix_exponential|Matrix exponential]], [[http://en.wikipedia.org/wiki/Exponential_map|Exponential map]] | ||
| - | |||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Square matrix]] | ||
