Matrix exponential

Set

context $ n\in\mathbb N $
definiendum $\mathrm{exp}: \text{SquareMatrix}(n,\mathbb C)\to\text{SquareMatrix}(n,\mathbb C)$
definiendum $\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: Matrix exponential, Exponential map

Parents

Context

Square matrix