For a continuous time Markov chain with finite state space and Markov transition function $p(t)$, its generator $G$ can be defined entry-wise as $$ G_{i,j}:=\lim_{t\to 0^+} \frac{p_{i,j}(t) - \delta_{i,j} }{t}, \forall \text{ states }i, j $$
$G$ can also be defined as $$G := \frac{dp(t)}{dt} |_{t=0^+}, $$ I was wondering what the matrix norm is in defining $\frac{dp(t)}{dt} |_{t=0^+}$ above?
Thanks and regards!