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chapter 17 of the book "Machine Learning - A Probabilistic Perspective" gives this figure

enter image description here

which is the probability of getting from i to j in exactly n steps. Obviously A(1) = A.

In the case of Figure 17.1 (b), the probability of getting from node 1 to node 3 in exactly 2 steps is

$A_{13}(2) = A_{12}(1)A_{23}(1)$

Is that correct?

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    $\begingroup$ Although it's correct, it's not very illuminating. The nature of the situation starts becoming apparent when you increase the number of steps. $\endgroup$
    – whuber ♦
    Commented Jul 25, 2019 at 10:57
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    $\begingroup$ You can get $n$-step transitions from discrete markov chain by exponentiating the transition matrix $\endgroup$
    – logistic
    Commented Jul 25, 2019 at 13:49
  • $\begingroup$ @logistic do you mean this. $A(n)=A^n$ ? $\endgroup$
    – czlsws
    Commented Jul 26, 2019 at 0:04
  • $\begingroup$ Yes @czlsws that's what I mean $\endgroup$
    – logistic
    Commented Jul 26, 2019 at 12:42
  • $\begingroup$ @logistic thanks for your comments. And how to apply that on "Figure 17.1 (b) node 1 to node 3" $\endgroup$
    – czlsws
    Commented Jul 26, 2019 at 22:14

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