So it's a vector-valued linear differential equation.

The solution is a natural generalization from the case where \\(D\\) contains just one element. In that case, the linear

\\[H: \mathbb{R}^1 \rightarrow \mathbb{R}^1\\]

amounts to multiplication by a constant \\(H\\), and the master equation takes the simple form:

\\[\Gamma'(t) = H \cdot \Gamma(t)\\]

which is an elementary differential equation, with solution:

\\[\Gamma(t) = e^{H t}\ \Gamma(0)\\]

The solution is a natural generalization from the case where \\(D\\) contains just one element. In that case, the linear

\\[H: \mathbb{R}^1 \rightarrow \mathbb{R}^1\\]

amounts to multiplication by a constant \\(H\\), and the master equation takes the simple form:

\\[\Gamma'(t) = H \cdot \Gamma(t)\\]

which is an elementary differential equation, with solution:

\\[\Gamma(t) = e^{H t}\ \Gamma(0)\\]