Hello,

Well, transition probabilities are the probabilities associated to the changes of state.

You calculate them with the information you're given. And they are (must be ?) conditional probabilities.

The transition matrix is , where

in the case of a non-homogenous Markov chain, the transition matrix varies according to n.

This transition matrix is made of the transition probabilities.

But I think google can also answer your question... with more precision for sure..