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As I mentioned in my comment, due to that you are searching for a method based on Python and ideally available in NumPy or SciPy, my suggestion is to use scipy.linalg.expm. It's really easy to use basically you have the $X$ matrix and you just pass it to the scipy.linalg.expm class and it would give you the exponential of $X$ (i.e. $e^{X}$). Due to that you ...

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