Apologies, I could have made this clearer. It is only those diagonal entries which are allowed to be negative. In fact they must be negative (or zero).
Technically, the diagonal entries are transitions from state i to i (ie. they are not really transitions but rather a measurement of “retention”). You can think of the positive or negative sign as indicating if it is a measure of transitioning away from the state, or retention in the state.
The diagonal entries are defined in another way. See the link:
https://en.wikipedia.org/wiki/Transition_rate_matrix#:~:text=In%20probability%20theory%2C%20a%20transition,Markov%20chain%20transitions%20between%20states.
Apologies, I could have made this clearer. It is only those diagonal entries which are allowed to be negative. In fact they must be negative (or zero).
Technically, the diagonal entries are transitions from state i to i (ie. they are not really transitions but rather a measurement of “retention”). You can think of the positive or negative sign as indicating if it is a measure of transitioning away from the state, or retention in the state.