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 matrix_exponential [2014/01/29 19:41]nikolaj matrix_exponential [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2014/01/29 19:41 nikolaj 2014/01/29 19:41 nikolaj 2013/12/21 19:57 external edit2013/09/19 21:19 nikolaj 2013/09/19 21:17 nikolaj 2013/09/19 21:16 nikolaj 2013/09/19 21:16 nikolaj old revision restored (2013/09/19 21:15)2013/09/19 21:15 nikolaj 2013/09/19 21:15 nikolaj 2013/09/19 21:15 nikolaj created Next revision Previous revision 2014/01/29 19:41 nikolaj 2014/01/29 19:41 nikolaj 2013/12/21 19:57 external edit2013/09/19 21:19 nikolaj 2013/09/19 21:17 nikolaj 2013/09/19 21:16 nikolaj 2013/09/19 21:16 nikolaj old revision restored (2013/09/19 21:15)2013/09/19 21:15 nikolaj 2013/09/19 21:15 nikolaj 2013/09/19 21:15 nikolaj created Line 1: Line 1: ===== Matrix exponential ===== ===== Matrix exponential ===== ==== Set ==== ==== 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 === === Theorems === - ^ $[A,​B]=0\implies \mathrm{exp}(A+B)=\mathrm{exp}(A)\mathrm{exp}(B)$ ^ + ^ $[A,​B]=0\implies \mathrm{exp}(A+B)=\mathrm{exp}(A)\cdot\mathrm{exp}(B)$ ^ === References === === References === Wikipedia: [[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]] [[Square matrix]]