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Is there any easy way to solve matrix differential equation?

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Nikolaos
Nikolaos 2012-8-28
i.e. i want to solve dp/dt = ip , where p is a matrix .
(my main problem is to solve solve dp/dt = ip + L(p) , where L is the liouvillian of an operator)
thank you in advance
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Nikolaos
Nikolaos 2012-8-30
Usually the dimensions are 36x36 of p . i is just imaginary constant number. L is an operator that involves a sum of matrices.

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Babak
Babak 2012-8-28
编辑：Babak 2012-8-28
The analytical solution to the problem of dp/dt = ip is
p(t) = C exp(it)
where C is a constant matrix same size as p used to determine the initial condition. i can be either a scalar or a matrix. If i is a matrix, in the above solution exp(it) will be a matrix as well which is defined in the literature.

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