I don't think such a thing is possible in the way you are hoping for.
My suggestion would be to find the Jordan normal form (and save the conjugating
matrix by passing `transformation=True`). Your matrix is diagonalizable so you
can then take a formal exponential of that (though you may have to do it "by
hand" e.g. diagonal_matrix([3^n,2^n])). You can then use the transformation
matrices to convert back to the correct form. Unfortunately, finding the
Jordan form finds numeric instead of exact eigenvalues even though it is
possible to find exact values in your case.
-Ivan
On Jan 24, 2013, at 3:57 PM, Christophe BAL <projet...@gmail.com> wrote:
> Hello,
> I would like, if it is possible, to calculate the formal power of one matrix ?
>
> My attempt is after but it doesn't work... :-(
>
> Christophe
>
> ======================
>
> var('n')
>
> assume(n, 'integer')
>
> E = matrix([
> [0 , 1 , 0 , 0 , 0 ],
> [1/4 , 0 , 3/4 , 0 , 0 ],
> [0 , 1/2 , 0 , 1/2 , 0 ],
> [0 , 0 , 3/4 , 0 , 1/4],
> [0 , 1 , 0 , 1 , 0 ]
> ])
>
> print E**n
>
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