Equation of motion from matrix

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To find the equation of motion from a Hamiltonian in matrix form, the approach depends on whether the system is classical or quantum. For classical mechanics, the Poisson bracket is essential for deriving the equations of motion. In quantum mechanics, it is necessary to decompose the Hamiltonian matrix into Dirac bra and ket eigenvectors. Understanding the context of the problem is crucial for selecting the appropriate method. Proper application of these techniques will yield the desired equations of motion.
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How can I find the equation of motion of a system with the Hamiltonian in matrix form?
 
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I assume given the nature of the question you are adept with the mathematics but I am unsure if you are dealing with a quantum or classical mechanics problem. If it is classical you need to use a Poisson bracket see http://ocw.mit.edu/ans7870/18/18.013a/textbook/chapter16/section03.html
If it is a quantum problem then decompose the matrix in Dirac bra and ket eigenvectors
 
Thank you.
 

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