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matrix_exponential [2013/12/21 19:57] 127.0.0.1 external edit |
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===== 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 === | ||
+ | ^ $[A,B]=0\implies \mathrm{exp}(A+B)=\mathrm{exp}(A)\cdot\mathrm{exp}(B)$ ^ | ||
=== 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]] |