===== Matrix exponential =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ n\in\mathbb N $ |

| @#FFBB00: definiendum | @#FFBB00: $\mathrm{exp}: \text{SquareMatrix}(n,\mathbb C)\to\text{SquareMatrix}(n,\mathbb C)$ |
| @#FFBB00: definiendum | @#FFBB00: $\mathrm{exp}(A):=\sum_{k=0}^\infty \frac{1}{k!} A^k $ |

==== Discussion ====
=== Theorems ===
^ $[A,B]=0\implies \mathrm{exp}(A+B)=\mathrm{exp}(A)\cdot\mathrm{exp}(B)$ ^
=== References ===
Wikipedia: [[http://en.wikipedia.org/wiki/Matrix_exponential|Matrix exponential]], [[http://en.wikipedia.org/wiki/Exponential_map|Exponential map]]

==== Parents ====
=== Context ===
[[Square matrix]]