On 01/24/13 08:57, Christophe BAL 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 ]
])
You guys probably won't like this answer. But Mathematica has a built
in command "MatrixPower:"
a = {{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}}
MatrixPower[N[a], n]
Note I convert a into its floating point representation, because
otherwise the solution is written in terms of the roots of the
characteristic polynomial, and while mathematica is perfectly happy to
write this down, it is a horribly length piece of output.
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