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matrix_exponential [2013/09/19 21:16] nikolaj |
matrix_exponential [2014/03/21 11:11] (current) |
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| ===== Matrix exponential ===== | ===== Matrix exponential ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ n\in\mathbb N $ | | + | | @#55CCEE: context | @#55CCEE: $ n\in\mathbb N $ | |
| - | | @#FFBB00: $\mathrm{exp}: \text{SquareMatrix}(n,\mathbb C)\to\text{SquareMatrix}(n,\mathbb C)$ | | + | | @#FFBB00: definiendum | @#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 $ | | + | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{exp}(A):=\sum_{k=0}^\infty \frac{1}{k!} A^k $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| + | === Theorems === | ||
| + | ^ $[A,B]=0\implies \mathrm{exp}(A+B)=\mathrm{exp}(A)\cdot\mathrm{exp}(B)$ ^ | ||
| === References === | === References === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Exponential_function|Exponential function]], [[http://en.wikipedia.org/wiki/Matrix_exponential|Matrix exponential]], [[http://en.wikipedia.org/wiki/Exponential_map|Exponential map]] | + | Wikipedia: [[http://en.wikipedia.org/wiki/Matrix_exponential|Matrix exponential]], [[http://en.wikipedia.org/wiki/Exponential_map|Exponential map]] |
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| - | [[Square matrix]], [[Infinite sum of complex numbers]], [[Factorial function]] | + | [[Square matrix]] |
