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We say that a stochastic matrix is regular iff $\exists n\in \mathbb N$ such that $p_{ij}(n)>0$ for all states $i,j$

How many powers of a matrix do we need to compute at most in order to verify that it is regular?

I think that we need to compute $n$ powers of the matrix but I don´t know if this is actually correct

I would appreciate if you can help me with this question

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  • $\begingroup$ Is $n$ the size of the matrix? $\endgroup$
    – Ben Grossmann
    Apr 29, 2016 at 4:29
  • $\begingroup$ Hint: if the chain is irreducible, what is the maximum possible distance between two states? If the chain is periodic, how does the period relate to the number of states? $\endgroup$
    – Ben Grossmann
    Apr 29, 2016 at 4:32
  • $\begingroup$ @Omnomnomnom, please look at my "similar" question, which has till now received no answer or comment on my approach. That question, if answered, will answer this one: math.stackexchange.com/questions/1762388/… $\endgroup$
    – Landon Carter
    Apr 29, 2016 at 6:58
  • $\begingroup$ You can find the answer here: math.stackexchange.com/questions/450090/… $\endgroup$
    – user940
    Apr 30, 2016 at 22:59

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