/sci/ - Science & Math

[Anonymous No.4048597]

>yfw wolfram alpha calculates the exponential of a matrix as the entrywise exponential of the matrix

http://www.wolframalpha.com/input/?i=e%5E%7B%7B4%2C%205%7D%2C%20%7B1%2F2%2C%201%2F3%7D%7D&t=crmt
b01

[Anonymous No.4048600]

>implying there is any other way to take e to the power of a matrix

[Anonymous No.4048606]

>>4048600
<div class="math">e^A=\sum_{k=0}^\infty \frac{A^k}{k!}</div>

[Anonymous No.4048607]

>>4048597
>matrix exponentiation
>hard math

[Anonymous No.4048620]

>>4048606

Let: <span class="math">\mathbf{A}\in\mathbb{M}_{n\times n}[/spoiler], then: <span class="math">\left(e^\mathbf{A}\right )_{j,k}=\sum_{p=0}^{\infty}\frac{1}{p!}~\underbrace{\sum_{i_1 =1}^n\sum_{i_2=1}^n\ldots\sum_{i_{p-1}=1}^n }_{p-1~times}a_{1,i_1}\left (\prod_{t=1}^{p-2}a_{i_t,i_{t+1}}\right )a_{i_{p-1},1}[/spoiler]

[Anonymous No.4048622]

>>4048606

Let: <span class="math">\mathbf{A}\in\mathbb{M}_{n\times n}[/spoiler], then: <span class="math">\left(e^\mathbf{A}\right )_{j,k}=\sum_{p=0}^{\infty}\frac{1}{p!}~\underbrace{\sum_{i_1 =1}^n\sum_{i_2=1}^n\ldots\sum_{i_{p-1}=1}^n }_{p-1~times}a_{j,i_1}\left (\prod_{t=1}^{p-2}a_{i_t,i_{t+1}}\right )a_{i_{p-1},k}[/spoiler]

[Josef crossed out the Atlantic !!nUf2NflSAyw No.4048646]

Classical example of the SISO principle: If you put shit in your computer, shit will come out of it.

Proper version:
http://www.wolframalpha.com/input/?i=MatrixExp%5B%7B%7B4%2C+5%7D%2C+%7B1%2F2%2C+1%2F3%7D%7D%5D

[Anonymous No.4048716]

>>4048646
you are right, but wolfram alpha is known for its capability to turn shit into gold. And seriously, what kind of purpose serves an entrywise exponential of a matrix?