- #1

- 9

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i.e. if there is a matrix A(t), how i can find exp(A(t)) ???

- Thread starter ranoo
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- #1

- 9

- 0

i.e. if there is a matrix A(t), how i can find exp(A(t)) ???

- #2

- 22,089

- 3,291

If it is neither of those, then you will want to triangulate your matrix to write it as a sum of a diagonizable matrix and a nilpotent matrix.

Did you have any particular matrixx in your mind?

- #3

- 1,444

- 4

It does not matter whether you matrix is "constant" or "non-constant". You define A=A(t) and calculate exp(A).

Added: Unless you have in mind so called http://en.wikipedia.org/wiki/Ordered_exponential" [Broken]

Added: Unless you have in mind so called http://en.wikipedia.org/wiki/Ordered_exponential" [Broken]

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- #4

- 9

- 0

0 t

I can't write the matrix but tha first row 0,1 and the second row 0,t

- #5

- 1,444

- 4

[tex]A(t)^n=\begin{pmatrix}0&t^{n-1}\\0&t^n\end{pmatrix}[/tex]

and

[tex]e^A(t)=\begin{pmatrix}1&0\\0&1\end{pmatrix}+\sum_{i=1}\frac{1}{n!}\begin{pmatrix}0&t^{n-1}\\0&t^n\end{pmatrix}[/tex]

I hope you will be able to finish. But better check the above. I could have made a mistake!

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